WAEC Mathematics Past Questions & Answers - Page 124

616.

In the diagram, the tangent MN makes an angle of 55^o with the chord PS. IF O is the centre of the circle, find < RPS

55^o

45^o

35^o

25^o

View answer & explanation

Correct answer is C

Join SR

< PRS = 90^o(Angle in a semicircle)

< PRS = 55^o (Angle between a chord and a tangent = Angle in the alternate segment)

< PSR + < PRS + < RSP = 180^o

90v + 55^o + < RSp = 180^o

< RSP = 180^o - 145^o

= 35^o

617.

In the diagram, < ROS = 66^o and < POQ = 3x. some construction lines are shown. Calculate the value of x.

10^o

11^o

22^o

35^o

View answer & explanation

Correct answer is B

From the diagram, OP bisects < ROS

< POS = \(\frac{1}{2}\) < ROS = \(\frac{1}{2}\) x 66^o

3x = 33^o

x = \(\frac{33^o}{3}\)

= 11^o

618.

In the diagram, triangles HKL and HIJ are similar. Which of the following ratios is equal to \(\frac{LH}{JH}\)

\(\frac{KL}{JI}\)

\(\frac{HK}{JK}\)

\(\frac{JI}{KL}\)

\(\frac{HK}{LK}\)

View answer & explanation

Correct answer is A

\(\bigtriangleup\) is similar to \(\bigtriangleup\) HIJ

< HKL = HJI = x^o

Hence, \(\frac{LH}{JH} = \frac{KH}{JH} \frac{KL}{IJ}\)

\(\frac{LH}{JH} = \frac{KL}{JI}\)

619.

In the diagram, QR//ST, /PQ/ = /PR/ and < PST = 75^o. Find the value of y

105^o

110^o

130^o

150^o

View answer & explanation

Correct answer is A

In \(\bigtriangleup\) PQR,

Q = S = 75^o (Corresponding angle)

R = Q = 75^o (Base angles of an isosceles \(\bigtriangleup\))

But, y + 75^o = 180^o (Sum of angles in a straight line)

y = 180 - 75

y = 105^o