1. The document defines different types of angles including acute, right, obtuse, straight, and reflex angles. It provides examples and definitions for each. 2. The document contains an exercise with questions about identifying, measuring, constructing, and drawing different angles. Students are asked to solve problems involving classifying angles, stating properties of angles, and using a protractor to measure and draw angles of various measures. 3. The exercise concludes with questions about calculating and drawing reflex angles, which are angles greater than 180 degrees but less than 360 degrees.

1.  𝐆𝐞𝐨𝐦𝐞𝐭𝐫𝐲 
Countdown Mathematics Class 5
Third Edition
𝐂𝐡𝐚𝐩𝐭𝐞𝐫 # 𝟕
𝐄𝐱𝐞𝐫𝐜𝐢𝐬𝐞 𝟕𝐚 𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧

2. 𝐍𝐨𝐭𝐞𝐬 𝐁𝐲: Adil Aslam 𝐒𝐮𝐛𝐣𝐞𝐜𝐭: Mathematics Class 5
1 | P a g e
𝐂𝐡𝐚𝐩𝐭𝐞𝐫 # 𝟕
𝐃𝐞𝐟𝐢𝐧𝐢𝐭𝐢𝐨𝐧𝐬
𝐍𝐨𝐭𝐞:
𝐖𝐫𝐢𝐭𝐞 𝐚𝐥𝐥 𝐃𝐞𝐟𝐢𝐧𝐢𝐭𝐢𝐨𝐧𝐬 𝐨𝐧 𝐲𝐨𝐮𝐫 𝐍𝐨𝐭𝐞𝐛𝐨𝐨𝐤.
𝐃𝐨 𝐚𝐥𝐥 𝐖𝐨𝐫𝐤 𝐍𝐞𝐚𝐭 𝐚𝐧𝐝 𝐂𝐥𝐞𝐚𝐧.
𝟏. 𝐀𝐧𝐠𝐥𝐞:
An angle is formed when two straight lines or rays meet at a common
endpoint. The common point of contact is called the vertex of an angle.
Example: An angle is represented by the symbol ∠. Here, the angle below is
∠AOB.
𝟐. 𝐀𝐜𝐮𝐭𝐞 𝐚𝐧𝐠𝐥𝐞:
An angle whose measure is less than 90 degrees.
Example:
𝟑. 𝐑𝐢𝐠𝐡𝐭 𝐚𝐧𝐠𝐥𝐞:
An angle whose measure is 90 degrees.
Example:
O
A
B

3. 𝐍𝐨𝐭𝐞𝐬 𝐁𝐲: Adil Aslam 𝐒𝐮𝐛𝐣𝐞𝐜𝐭: Mathematics Class 5
2 | P a g e
𝟒. 𝐎𝐛𝐭𝐮𝐬𝐞 𝐚𝐧𝐠𝐥𝐞:
An angle whose measure is greater than 90° but less than 180° is called an
obtuse angle.
Example:
𝟔. 𝐒𝐭𝐫𝐚𝐢𝐠𝐡𝐭 𝐚𝐧𝐠𝐥𝐞:
An angle whose measure is 180° is called a straight angle.
Example:
𝟕. 𝐑𝐞𝐟𝐥𝐞𝐱 𝐚𝐧𝐠𝐥𝐞:
An angle whose measure is more than 180° but less than 360° is called a
reflex angle.
Example:
𝟖. 𝐂𝐨𝐦𝐩𝐥𝐞𝐭𝐞 𝐚𝐧𝐠𝐥𝐞:
A complete angle is equal to 360°.
Example:

4. 𝐍𝐨𝐭𝐞𝐬 𝐁𝐲: Adil Aslam 𝐒𝐮𝐛𝐣𝐞𝐜𝐭: Mathematics Class 5
3 | P a g e
𝐄𝐱𝐞𝐫𝐜𝐢𝐬𝐞 𝟕𝐚
𝐏𝐚𝐠𝐞 # 𝟏𝟏𝟗 , 𝟏𝟐𝟎 , 𝟏𝟐𝟏
𝐍𝐨𝐭𝐞:
𝐐𝐮𝐞𝐬𝐭𝐢𝐨𝐧 # 𝟏 , 𝟐 , 𝟑 , 𝟒 , 𝟕 , 𝟗 𝐒𝐨𝐥𝐯𝐞 𝐨𝐧 𝐁𝐨𝐨𝐤.
𝐐𝐮𝐞𝐬𝐭𝐢𝐨𝐧 # 𝟓 , 𝟔 , 𝟖 𝐒𝐨𝐥𝐯𝐞 𝐨𝐧 𝐍𝐨𝐭𝐞𝐛𝐨𝐨𝐤.
𝐃𝐨 𝐚𝐥𝐥 𝐖𝐨𝐫𝐤 𝐍𝐞𝐚𝐭 𝐚𝐧𝐝 𝐂𝐥𝐞𝐚𝐧.
𝟏. 𝐅𝐢𝐥𝐥 𝐢𝐧 𝐭𝐡𝐞 𝐛𝐥𝐚𝐧𝐤𝐬.
𝐚. An acute angle is any angle greater than 0° but less than _______________.
𝐛. An angle which is greater than a right angle but less than 180° is called an
__________________ angle.
𝐜. A reflex angle is any angle which is greater than ____________ but less than __________.
𝐝. Two right angles make a _____________________ angle.
𝐞. The arms of a right angle meet each other at ______________________.
𝟐. 𝐒𝐭𝐚𝐭𝐞 𝐰𝐡𝐞𝐭𝐡𝐞𝐫 𝐭𝐡𝐞 𝐟𝐨𝐥𝐥𝐨𝐰𝐢𝐧𝐠 𝐚𝐫𝐞 𝐭𝐫𝐮𝐞 𝐨𝐫 𝐟𝐚𝐥𝐬𝐞.
𝐚. A reflex angle is greater than 180° and less than 360°. ( __________ )
𝐛. The sum of all the angles on a line add up to 180°. ( __________ )
𝐜. Angles at a point add up to 180°. ( ___________ )
𝐝. The point where two arms of the angle meet is called the vertex. ( ____________ )
𝐞. There are 90 degrees in straight angle. ( ___________ )
𝟗𝟎°
𝐓
𝐅
𝐅
𝐎𝐛𝐭𝐮𝐬𝐞
𝟏𝟖𝟎° 𝟑𝟔𝟎°
𝐒𝐭𝐫𝐚𝐢𝐠𝐡𝐭
𝟗𝟎°
𝐓
𝐓

5. 𝐍𝐨𝐭𝐞𝐬 𝐁𝐲: Adil Aslam 𝐒𝐮𝐛𝐣𝐞𝐜𝐭: Mathematics Class 5
4 | P a g e
𝟑. 𝐒𝐞𝐥𝐞𝐜𝐭 𝐭𝐡𝐞 𝐜𝐨𝐫𝐫𝐞𝐜𝐭 𝐚𝐧𝐬𝐰𝐞𝐫 𝐟𝐫𝐨𝐦 𝐭𝐡𝐞 𝐠𝐢𝐯𝐞𝐧 𝐨𝐩𝐭𝐢𝐨𝐧𝐬.
𝐚. An angle greater than 0° and less than 90° is:
 an obtuse angle  a right angle
 a straight angle  an acute angle
𝐛. An angle greater than 180° and less than 360° is:
 a right angle  a reflex angle
 an obtuse angle  an acute angle
𝐜. The magnitude of a reflex angle adjacent to ∠ABC is:
 90° − ∠ABC  180° − ∠ABC
 90° + ∠ABC  360° − ∠ABC
𝐝. An angle with magnitude 360° − 252° is:
 obtuse angle  straight angle
 reflex angle  acute angle
𝐞. The number of right angles in a straight line are:
 one  two
 three  four
𝟒. 𝐌𝐞𝐚𝐬𝐮𝐫𝐞 𝐭𝐡𝐞 𝐟𝐨𝐥𝐥𝐨𝐰𝐢𝐧𝐠 𝐚𝐧𝐠𝐥𝐞𝐬 𝐰𝐢𝐭𝐡 𝐭𝐡𝐞 𝐡𝐞𝐥𝐩 𝐨𝐟 𝐚 𝐩𝐫𝐨𝐭𝐫𝐚𝐜𝐭𝐨𝐫.
𝐚. 𝐛.
✓
✓
✓
✓
✓
30° 60°

6. 𝐍𝐨𝐭𝐞𝐬 𝐁𝐲: Adil Aslam 𝐒𝐮𝐛𝐣𝐞𝐜𝐭: Mathematics Class 5
5 | P a g e
𝐜. 𝐝.
𝟓. 𝐂𝐨𝐧𝐬𝐭𝐫𝐮𝐜𝐭 𝐭𝐡𝐞 𝐟𝐨𝐥𝐥𝐨𝐰𝐢𝐧𝐠 𝐚𝐧𝐠𝐥𝐞𝐬.
𝐚. ∠ABC (right angle)
𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧:
𝐛. ∠STU (acute angle)
𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧:
𝐜. ∠EFG (reflex angle)
𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧:
45°
90°
3 6 0°
− 2 6 0°
1 0 0°

7. 𝐍𝐨𝐭𝐞𝐬 𝐁𝐲: Adil Aslam 𝐒𝐮𝐛𝐣𝐞𝐜𝐭: Mathematics Class 5
6 | P a g e
𝐝. ∠PQR (obtuse angle)
𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧:
𝟔. 𝐃𝐫𝐚𝐰 𝐭𝐡𝐞𝐬𝐞 𝐚𝐧𝐠𝐥𝐞𝐬, 𝐮𝐬𝐢𝐧𝐠 𝐭𝐡𝐞 𝐩𝐫𝐨𝐭𝐫𝐚𝐜𝐭𝐨𝐫.
𝐚. 40°
𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧:
𝐛. 90°
𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧:

8. 𝐍𝐨𝐭𝐞𝐬 𝐁𝐲: Adil Aslam 𝐒𝐮𝐛𝐣𝐞𝐜𝐭: Mathematics Class 5
7 | P a g e
𝐜. 55°
𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧:
𝐝. 60°
𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧:
𝐞. 115°
𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧:
𝐟. 145°
𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧:

9. 𝐍𝐨𝐭𝐞𝐬 𝐁𝐲: Adil Aslam 𝐒𝐮𝐛𝐣𝐞𝐜𝐭: Mathematics Class 5
8 | P a g e
𝟕. 𝐂𝐚𝐥𝐜𝐮𝐥𝐚𝐭𝐞 𝐭𝐡𝐞𝐬𝐞 𝐫𝐞𝐟𝐥𝐞𝐱 𝐚𝐧𝐠𝐥𝐞𝐬 𝐮𝐬𝐢𝐧𝐠 𝐭𝐡𝐞 𝐩𝐫𝐨𝐭𝐫𝐚𝐜𝐭𝐨𝐫.
𝐚. 𝐛.
𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧: 𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧:
𝐜. 𝐝.
𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧: 𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧:
3 6 0°
− 1 3 0°
2 3 0°
3 6 0°
− 3 0°
3 3 0°
3 6 0°
− 9 0°
2 7 0°
3 6 0°
− 6 0°
3 0 0°

10. 𝐍𝐨𝐭𝐞𝐬 𝐁𝐲: Adil Aslam 𝐒𝐮𝐛𝐣𝐞𝐜𝐭: Mathematics Class 5
9 | P a g e
𝟖. 𝐃𝐫𝐚𝐰 𝐭𝐡𝐞𝐬𝐞 𝐫𝐞𝐟𝐥𝐞𝐱 𝐚𝐧𝐠𝐥𝐞𝐬 𝐰𝐢𝐭𝐡 𝐭𝐡𝐞 𝐡𝐞𝐥𝐩 𝐨𝐟 𝐩𝐫𝐨𝐭𝐫𝐚𝐜𝐭𝐨𝐫.
𝐚. Reflex ∠PQR = 320°
𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧:
𝐛. Reflex ∠WXY = 290°
𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧:
𝐜. Reflex ∠CDE = 335°
𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧:
3 6 0°
− 3 2 0°
4 0°
3 6 0°
− 2 9 0°
7 0°
3 6 0°
− 3 3 5°
2 5°

11. 𝐍𝐨𝐭𝐞𝐬 𝐁𝐲: Adil Aslam 𝐒𝐮𝐛𝐣𝐞𝐜𝐭: Mathematics Class 5
10 | P a g e
𝐝. Reflex ∠ABC = 200°
𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧:
𝟗. 𝐈𝐝𝐞𝐧𝐭𝐢𝐟𝐲 𝐭𝐡𝐞 𝐚𝐧𝐠𝐥𝐞𝐬 𝐚𝐬 𝐬𝐦𝐚𝐥𝐥𝐞𝐫 𝐭𝐡𝐚𝐧 𝟗𝟎° 𝐚𝐧𝐝 𝐠𝐫𝐞𝐚𝐭𝐞𝐫 𝐭𝐡𝐚𝐧 𝟗𝟎°
𝐢𝐧 𝐭𝐡𝐞 𝐟𝐨𝐥𝐥𝐨𝐰𝐢𝐧𝐠 𝐟𝐢𝐠𝐮𝐫𝐞𝐬.
𝐚. 𝐛. 𝐜.
𝐝. 𝐞. 𝐟.
𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧:
a. Smaller than 90°
b. Greater than 90°
c. Smaller than 90°
d. Smaller than 90°
e. Greater than 90°
f. Smaller than 90°
3 6 0°
− 2 0 0°
1 6 0°