This is the Grade 4 Mathematics Quarter 3 Module 2, “Kinds of Angles,” a self-learning module (SLM) from DepEd Region V (Alternative Delivery Mode, First Edition, 2020). It is for Grade 4 learners studying at home or in class, and for the parents and teachers who guide them. After the module, learners can tell right, acute, and obtuse angles apart by their measures, describe each one, and draw them.
On this page 7 sections
What learners will learn
The module explains that angles are formed when two lines intersect, and it sorts angles by their measures. By the end of the module, learners should be able to:
- Identify the kinds of angles (right, acute, and obtuse).
- Describe the different kinds of angles.
- Illustrate the different kinds of angles.
Parts of the module
The module has one lesson, Lesson 1: Kinds of Angles, arranged in the usual SLM parts:
- What I Know (pretest): matching angle names to their measures, matching pictures (a staircase, scissors, a clock, the letter H) to kinds of angles, and drawing one of each angle.
- What’s In: a review of parallel, intersecting, and perpendicular lines, with an identifying activity and a drawing activity.
- What’s New: a short story about Lola Remy, Lola Inday, and Lola Nancy, who take their vitamins at 9:00, 2:00, and 5:00. Learners draw the clock hands at those times.
- What is It: the lesson itself, using the three clocks to define each kind of angle and showing how to name an angle.
- What’s More: identifying five angles and drawing named angles such as acute angle NOP and right angle PQR.
- What I Have Learned: a summary of the three definitions.
- What I Can Do: naming the kind of angle formed by rays coming out from one point, A.
- Assessment: identifying seven angles and describing each kind of angle.
- Additional Activities: classifying ten angles from their measures in degrees.
- Answer Key for the activities and tests.
The three kinds of angles
The module uses the hands of a clock to show each kind of angle:
| Time on the clock | Angle formed by the hands | Kind of angle | Rule |
|---|---|---|---|
| 9:00 (Lola Remy) | 90° | Right angle | Measures exactly 90° |
| 2:00 (Lola Inday) | 60° | Acute angle | Measures between 0° and 90° |
| 5:00 (Lola Nancy) | 150° | Obtuse angle | Measures between 90° and 180° |
To classify any angle, compare its measure with 90°:
- Exactly 90° means a right angle, for example 90°.
- Less than 90° means an acute angle, for example 48°, 64°, or even 89°.
- More than 90° but less than 180° means an obtuse angle, for example 96°, 125°, or 179°.
These examples come from the module’s Additional Activities, where learners classify ten angles in this way.
How to name an angle
An angle is formed by two rays with a common endpoint. In the module’s example, rays BA and BC share the endpoint B and form angle ABC.
- In symbols, it is written ∠ABC and read as “angle ABC.”
- It may also be written ∠CBA. The letter of the common endpoint always stays in the middle.
- It may also be named with a number, ∠1, or simply by its endpoint, ∠B.
Learners use this naming in the activities, for example when they draw “obtuse angle HIJ” or name the kind of angle ∠EAB in the What I Can Do part.
How to use this module
The module asks learners to write all answers on a separate sheet of paper and not to mark the module itself.
- Learners: Start with the pretest. If you got 8 or higher, the module says the lesson will be easy for you. If you got lower than 8, study the lesson and exercises carefully. Go through the parts in order, then answer the Assessment and Additional Activities. After the Additional Activities, a score of 8 to 10 means you are ready for the next module. A lower score means you should go over the lessons and exercises again. Check your work with the answer key honestly.
- Parents and facilitators: Help your child read the directions before each task. A real clock at home is an easy way to show the 9:00, 2:00, and 5:00 angles from the lesson.
- Teachers: The pretest, Assessment, and Additional Activities give quick checks of whether learners can identify, describe, and draw each kind of angle. Learners who have trouble can go back to the What’s In review of perpendicular lines, since perpendicular lines form right angles.
Frequently asked questions
What grade and quarter is the Kinds of Angles module for?
It is Grade 4 Mathematics, Quarter 3, Module 2. It was produced by DepEd Region V as an Alternative Delivery Mode module, First Edition, 2020.
What are the three kinds of angles in this module?
A right angle measures exactly 90°. An acute angle measures between 0° and 90°. An obtuse angle measures between 90° and 180°.
How does the module use a clock to teach angles?
At 9:00 the clock hands form a 90° right angle. At 2:00 they form a 60° acute angle, and at 5:00 they form a 150° obtuse angle.
How do you name an angle such as angle ABC?
An angle formed by rays BA and BC with common endpoint B is written ∠ABC or ∠CBA. It can also be named ∠B or with a number such as ∠1.
Does the module have an answer key?
Yes. The module includes answers for the pretest, the activities, the Assessment, and the Additional Activities.
Full text of the module
The text below is a transcription of the PDF above, as printed.
Mathematics Quarter 3 – Module 2: Kinds of Angles
[illustration: group of students and a teacher studying outdoors and at a table, with a globe and a student writing by a lamp]
Mathematics – Grade 4 Alternative Delivery Mode Quarter 3 – Module 2: Kinds of Angles First Edition, 2020
Republic Act 8293, section 176 states that: No copyright shall subsist in any work of the Government of the Philippines. However, prior approval of the government agency or office wherein the work is created shall be necessary for exploitation of such work for profit. Such agency or office may, among other things, impose as a condition the payment of royalties.
Borrowed materials (i.e., songs, stories, poems, pictures, photos, brand names, trademarks, etc.) included in this module are owned by their respective copyright holders. Every effort has been exerted to locate and seek permission to use these materials from their respective copyright owners. The publisher and authors do not represent nor claim ownership over them.
Published by the Department of Education Secretary: Leonor Magtolis Briones Undersecretary: Diosdado M. San Antonio
Development Team of the Module
Writer: Narlyn J. Dechavez Editors: Loyd H. Botor, Elena D. Hubilla Reviewers: Loyd H. Botor, Elena D. Hubilla Illustrator: Jason C. Borabo Layout Artist: Cherry Lou O. Calison Management Team: Gilbert T. Sadsad, Francisco B. Bulalacao Jr., Grace U. Rabelas, Ma Leilani R. Lorico, Monserat D. Guemo, Florena M. Deuna
Printed in the Philippines by ________________________
Department of Education – Region V
Office Address : Regional Center Site, Rawis, Legazpi City, 4500 Telefax : 0917-178-1288 E-mail Address : region5@deped.gov.ph
Mathematics Quarter 3 – Module 2: Kinds of Angles
Introductory Message
This Self-Learning Module (SLM) is prepared so that you, our dear learners, can continue your studies and learn while at home. Activities, questions, directions, exercises, and discussions are carefully stated for you to understand each lesson.
Each SLM is composed of different parts. Each part shall guide you step-by-step as you discover and understand the lesson prepared for you.
Pre-tests are provided to measure your prior knowledge on lessons in each SLM. This will tell you if you need to proceed on completing this module or if you need to ask your facilitator or your teacher’s assistance for better understanding of the lesson. At the end of each module, you need to answer the post-test to self-check your learning. Answer keys are provided for each activity and test. We trust that you will be honest in using these.
In addition to the material in the main text, Notes to the Teacher are also provided to our facilitators and parents for strategies and reminders on how they can best help you on your home-based learning.
Please use this module with care. Do not put unnecessary marks on any part of this SLM. Use a separate sheet of paper in answering the exercises and tests. And read the instructions carefully before performing each task.
If you have any questions in using this SLM or any difficulty in answering the tasks in this module, do not hesitate to consult your teacher or facilitator.
Thank you.
What I Need to Know
Angles are formed when two lines intersect.
In this lesson, you will learn about the different kinds of angles based on their measures. The first activity will allow you to explore and discover the different kinds of angles which the hour and minute hands of a clock form. The succeeding activities, in turn, will help you describe and illustrate the different kinds of angles.
At the end of this module, you should be able to:
- Identify the kinds of angles (right, acute and obtuse).
- Describe the different kinds of angles.
- Illustrate the different kinds of angles.
REMINDER: In all of the activities, please write your answers on a separate sheet of paper.
What I Know
A.
Match the descriptions listed in the second column with the angles in the first column. Write the letter of the correct answer on your answer sheet.
| A | B |
|---|---|
| ___ 1. Acute angle | a. Measures between 90° and 180° |
| ___ 2. Right Angle | b. Measures between 0° and 90° |
| ___ 3. Obtuse Angle | c. Measures exactly 90° |
| d. Measures exactly 180° |
B.
Match the different kinds of angles listed in Column B with the angles shown or represented by the pictures in Column A. Write the letter of the correct answer on the blank provided in your answer sheet.
| Column A | Column B |
|---|---|
| _____1. [illustration: staircase with handrail, shown with a curved dashed path] | A. Right Angle |
| _____ 2. [illustration: pair of scissors] | B. Obtuse Angle |
| _____ 3. [illustration: clock face with two hands] | C. Acute Angle |
| _____ 4. [illustration: bold block letter H] |
C.
Draw an example of each kind of angle.
- acute angle
- right angle
- obtuse angle
If you got 8 or higher, that is VERY GOOD. The lesson in this module will be easy for you. If you got lower than 8, you have to study carefully the lesson and the exercises given.
Lesson 1: Kinds of Angles
What’s In
Activity 1
Identify each as parallel, intersecting or perpendicular lines.
- [illustration: two lines crossing diagonally, each with arrowheads at both ends] ______________
- [illustration: two horizontal parallel lines, each with arrowheads at both ends] ______________
- [illustration: a horizontal line and a vertical line crossing, each with arrowheads at both ends] ______________
Activity 2
Draw examples of parallel, perpendicular and intersecting lines.
- Parallel lines
- Intersecting lines
- Perpendicular lines
What’s New
To maintain their healthy bodies, Lola Remy, Lola Inday and Lola Nancy drink their vitamins everyday. Lola Remy drinks her vitamins at exactly 9:00 in the morning, Lola Inday at 2:00 and Lola Nancy at 5:00 in the afternoon.
a. Who drink their vitamins everyday? Why do they drink their vitamins everyday? b. At what time do they drink their vitamins? c. Draw the positions of the hour and minute hands of the clock at those times given below.
- 9:00
- 2:00
- 5:00
What is It
Let’s take a look at the clocks showing the respective times Lola Remy, Lola Inday and Lola Nancy take their vitamins.
[illustration: clock face showing 9:00, with hour and minute hands forming a right angle]
Lola Remy
- At 9:00, the minute and hour hands of the clock form an angle which measures 90˚. This angle, like all angles which measure 90˚, is called a right angle.
Lola Inday
[illustration: clock face showing 2:00 with hour and minute hands]
- At 2:00, the minute and hour hands of the clock form an angle which measures 60˚. This is between 0˚ and 90˚ The angle here, like all other angles which measure between 0˚ and 90˚, is called an acute angle.
[illustration: clock face showing 5:00 with hour and minute hands]
Lola Nancy
- At 5:00, the minute and hour hands of the clock form an angle which measures 150˚. This is between 90˚ and 180˚ The angle here, like all other angles which measure between 90˚ and 180˚, is called an obtuse angle.
An angle is formed by two rays with a common endpoint.
In the figure below, Rays BA and BC have B as their common endpoint and they form angle ABC. Using symbols, we write ∠ABC, which is read as “angle ABC”. The angle may also be called ∠CBA.
[illustration: angle with vertex B and rays BA and BC, labeled A, B, C, with the angle marked 1]
The angle above may also be named as ∠1, or simply ∠B.
What’s More
Activity 1
Identify each angle as acute, right or obtuse.
- [illustration: angle formed by two rays] _____
- [illustration: angle formed by two rays] _____
- [illustration: angle formed by two rays] _____
- [illustration: angle formed by two rays] _____
- [illustration: angle formed by two rays] _____
Activity 2
Draw the required angle.
- acute angle NOP
- right angle PQR
- obtuse angle HIJ
- right angle ABC
- acute angle JKL
What I Have Learned
Remember:
A right angle measures exactly 90˚. An acute angle measures between 0º and 90º. An obtuse angle measures between 90º and 180º.
What I Can Do
Direction: What kind of angles are the following?
- ∠EAB _________________
- ∠ GAC _________________
- ∠CAH _________________
- ∠DAI _________________
- ∠GAB _________________
[illustration: eight rays radiating from point A, labeled E (up), F (upper right), B (right), H (lower right), D (down), I (lower left), C (left), G (upper left)]
Assessment
I. Identify each of the following by writing acute, right or obtuse angle in the blank.
- [illustration: angle formed by two rays] _____
- [illustration: angle formed by two rays] _____
- [illustration: angle formed by two rays] _____
- [illustration: angle formed by two rays] _____
- [illustration: angle formed by two rays] _____
- [illustration: angle formed by two rays] _____
- [illustration: angle formed by two rays] _____
II. Describe the following angles.
- acute angle
- obtuse angle
- right angle
Additional Activities
What kind of angles are the following?
- 48˚ _______________
- 125˚ _______________
- 90˚ _______________
- 105˚ _______________
- 64˚ _______________
- 89˚ _______________
- 96˚ _______________
- 167˚ _______________
- 179˚ _______________
- 77˚ _______________
Please check your answers with the ANSWER KEY on page 10.
Got a score of 8-10? CONGRATULATIONS! Job well done. See you in the next module. If below 8, you may have to go over the lessons and the exercises again.
Answer Key
What’s New
A. Lola Remy, Lola Inday and Lola Nancy. To maintain their healthy body.
B. 9:00 in the morning, 2:00 and 5:00 in the afternoon.
C. 9:00, 2:00, and 5:00
[illustration: three clock faces showing 9:00, 2:00 and 5:00]
Assessment
I.
- acute angle
- right angle
- obtuse angle
- acute angle
- right angle
- acute angle
- right angle
II.
- Acute angle measures between 0˚ and 90˚.
- Obtuse angle measures between 90˚ and 180˚.
- Right angle measures exactly 90˚.
What I Can Do
- Right Angle
- Obtuse Angle
- Obtuse Angle
- Acute Angle
- Acute Angle
Additional Activities
- Acute Angle
- Obtuse Angle
- Right Angle
- Obtuse Angle
- Acute Angle
- Acute Angle
- Obtuse Angle
- Obtuse Angle
- Obtuse Angle
- Acute Angle
What’s More
Activity 1
- Acute angle
- Right angle
- Obtuse angle
- Acute angle
- Obtuse angle
Activity 2
[illustration: answer drawings of angles NOP, PQR, HIJ, ABC and JKL, with letters labeled]
What’s In
Activity 1
- Intersecting Lines
- Parallel Lines
- Perpendicular Lines
Activity 2
- [illustration: two parallel lines]
- [illustration: two intersecting lines]
- [illustration: two perpendicular lines]
What I Know
A. B. C.
- b 1. b
- c 2. c
- a 3. b
- a
[transcriber’s note: this page is printed upside down, and the column alignment of the What I Know answer grid is not certain; the values are given in the order they appear]
References
Electronic Sources:
Department of Education. “DepEd Order No. 12, s. 2020. Adoption of the Basic Education Learning Continuity Plan for SY 2020-2021 In Light of the Covid-19 Public Health Emergency”. Accessed June 19, 2020. p. 342. https://www.deped.gov.ph/2020/06/19/june-19-2020-do012-2020-adoption-of-the-basic-education-learningcontinuity-plan-for-school-year-2020-2021-in-the-light-ofthe-covid-19-public-health-emergency/
Mathisfun. “Angles”. https://www.mathsisfun.com/angles.html
For inquiries or feedback, please write or call:
Department of Education – Bureau of Learning Resources (DepEd-BLR)
Ground Floor, Bonifacio Bldg., DepEd Complex Meralco Avenue, Pasig City, Philippines 1600
Telefax: (632) 8634-1072; 8634-1054; 8631-4985
Email Address: blr.lrqad@deped.gov.ph * blr.lrpd@deped.gov.ph
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