In the diagram, ∠ PSR = 220°, ∠ SPQ = 58° and ∠ PQR =

MATHEMATICS

WAEC 2010

In the diagram, ∠ PSR = 220°, ∠ SPQ = 58° and ∠ PQR = 41°. Calculate the obtuse angle QRS.

A. 90°
B. 100°
C. 121°
D. 60°

Correct Answer: C. 121°

Explanation

Joining SQ. In \(\bigtriangleup\) SPQ,

(22^o + a) + 55^o + (41^o + b) = 180^o

121^o + a + b = 180^o

a + b = 180 - 121

a + b = 59^o.....(1)

In \(\bigtriangleup\) SRPQ; R + a + b = 180^o

R + 59^o = 180^o

(in (1), a + b = 59^o)

R = 180 - 59

R = 121^o

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