WAEC Mathematics Past Questions & Answers - Page 31

151.

In the diagram, PQR is a circle with center O. If OPQ = 48°, find the value of M.

A.

96\(^o\)

B.

90\(^o\)

C.

68\(^o\)

D.

42\(^o\)

Correct answer is A

< O\(Q\)P = 48\(^o\) (base angles of isoceles \(\triangle\))

m = 48\(^o\) + 48\(^o\) = 96\(^o\) (exterior angle of a \(\triangle\))

153.

The length of an arc of a circle of radius 3.5 cm is  1\(\frac{19}{36}\) cm. Calculate, correct to the nearest degree , the angle substended by the centre of the circle. [Take \(\pi = \frac{22}{7}\)] 

A.

55\(^o\)

B.

36\(^o\)

C.

25\(^o\)

D.

22\(^o\)

Correct answer is C

L = \(\frac{\theta}{360^o}\) = 2\(\pi\)

\(\frac{55}{36} = \frac{\theta}{360^o} \times 2 \times \frac{22}{7} \times 3.5\)

\(\theta = \frac{360 \times 55 \times 44 \times 0.5}{3 \times 44 \times 0.5}\)

= \(\theta = 25^o\)

154.

In the diagram, \(\overline{MN}\)//\(\overline{PQ}\), < MNP = 2x, and < NPQ = (3x - 50)°. Find the value of < NPQ 

A.

200\(^o\)

B.

100\(^o\)

C.

120\(^o\)

D.

90\(^o\)

Correct answer is B

 

2x = 3x - 50 alternate angle 

50\(^o\) = 3x - 2x 

50\(^o\) = x 

< NPQ = (3x - 50)\(^o\) 

= 3(500)\(^o\) - 50 

= 150 - 50 = 100\(^o\) 

155.

Each interior angle of a regular polygon is 168\(^o\). Find the number of sides of the polygon 

A.

30

B.

36

C.

24

D.

18

Correct answer is A

Exterior angle = 180\(^o\) - 168\(^o\)

Number of sides = \(\frac{360^o}{12}\)

= 30\(^o\)