Countdown Maths Class 5 Chapter # 7 Solution. All Classs 4 to 7 , 9 , 10 Notes Available.

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°