Lessons on Angles, Triangle and Polygon for students preparing for WASSCE, NECO and JAMB exams for secondary schools in West Africa.

1. Worked
Examples
Multiple
Choice
Practice
Questions
Lesson
Notes EXIT

2. < 𝑄𝑇𝑃 = 320
Triangle PQT is isosceles. The base angles of isosceles
triangle are equal.
⇒ < 𝑃𝑄𝑇 = 1800
− 320
+ 320
= 1160
Angles on a straight line add up to1800
.< 𝑃𝑄𝑇 and < 𝑇𝑄𝑅
are on a straight line .
⇒ < 𝑇𝑄𝑅 = 1800
− 1160
= 640
Triangle QRT is also
isosceles
< 𝑇𝑅𝑄 =< 𝑇𝑄𝑅 = 640
Angles on a straight line
< 𝑇𝑅𝐾 +< 𝑇𝑅𝑄 = 1800
⇒ < 𝑇𝑅𝐾 = 1800
− 640
= 1160
In the diagram above, <TPQ=320
and |PQ|=|QT|=|TR|.
Calculate < TRK.

3. 𝑎𝑛 𝑒𝑥𝑡𝑒𝑟𝑖𝑜𝑟 𝑎𝑛𝑔𝑙𝑒 𝑒𝑞𝑢𝑎𝑙𝑠 𝑡ℎ𝑒 𝑠𝑢𝑚 𝑜𝑓 𝑡ℎ𝑒 𝑡𝑤𝑜 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑖𝑛𝑡𝑒𝑟𝑖𝑜𝑟 𝑎𝑛𝑔𝑙𝑒𝑠
⇒ 600
+ 400
= < 𝑃𝑂𝑁
⇒< 𝑃𝑂𝑁 = 1000
⇒ 𝑆𝑖𝑛𝑐𝑒 𝑀𝑁 𝑖𝑠 𝑝𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 𝑡𝑜 𝐾𝐿,
𝑖𝑡 𝑚𝑒𝑎𝑛𝑠 𝑡ℎ𝑎𝑡 < 𝑃𝑂𝑁 𝑐𝑜𝑟𝑟𝑒𝑠𝑝𝑜𝑛𝑑𝑠 𝑡𝑜 < 𝑃𝐾𝐿
𝐴𝑙𝑠𝑜, 𝑐𝑜𝑟𝑟𝑒𝑠𝑝𝑜𝑛𝑑𝑖𝑛𝑔 𝑎𝑛𝑔𝑙𝑒𝑠 𝑎𝑟𝑒 𝑒𝑞𝑢𝑎𝑙
𝐻𝑒𝑛𝑐𝑒 , < 𝑃𝐾𝐿 = 1000
In the diagram above MN is parallel to KL. If
angle NMP is 600
and angle MPK is400
.
Calculate the value of angle PKL.
𝑊𝐴𝑆𝑆𝐶𝐸, 2005.

4. In the figure QRS is an equilateral triangle and QRT is
an isosceles triangle. If angle QRT=470
, what is the
value of y.
A .13 𝑂
B .15°
C . 25°
D .23°
E. 33°
EXIT
MCQ
470

5. In the diagram below, 𝑃𝑄||𝑅𝑆. Find the value of 𝑧
B .85°
A 75°
C 44°
D .64°
E .35°
EXIT
MCQ
B

6. Consider the diagram. What is the value of x?
D .20°
A 25°
C 40°
B .10°
E .30°
EXIT
MCQ
B

7. Which of the following is true?
D. The sum of the interior angle of a triangle is
equal to two right angles
A . The two smaller angles of a right angle triangle
are supplementary
C. 300
𝑎𝑛𝑑 1500
are complementary angles
°
B. The sum of the exterior angle of a regular polygon
is1800
.
E. 300
𝑎𝑛𝑑 900
are complementary
angles EXIT
MCQ
B

8. The formula,
3600
𝑛
gives the value of ……… angle of a
regular polygon.
E. each exterior
A the sum of the exterior
C. the sum of the interior
B. the product of the interior
D. exterior
EXIT
MCQ
B

9. Three times the sum of the exterior angles of a regular
polygon is the sum of the interior angles of the polygon.
What is the name of the polygon?
B. Octagon
A. Hexagon
C. Pentagon
E. Heptagon
D. Decagon
EXIT
MCQ

10. Find the sum of the interior angles of a heptagon?
E. 900°
A 800°
C. 540°
B 720°
D. 1080°
EXIT
MCQ

11. The sum of the exterior angles of an n-sided polygon is
….
B. 360°
A. 𝑛 − 2 1800
C 𝑛−2 1800
𝑛
B 180°
D. 3600
𝑛
EXIT
MCQ

12. What is the value of 𝑥?
B. 135°
A 15°
C. 35°
B 45°
D. 45°
EXIT
MCQ

13. EXIT

14. The sum of angles on a straight line is
180° EXIT
The sum of angles around a point is 180°

15. The equilateral triangle has all sides equal and each
angle is 60°
EXIT

16. The isosceles triangles has two sides and angles
equal
EXIT

17. EXIT