The diagram shows a trapezium inscribed in a semi-circle. If O is the mid-point of WZ and |WX| = |XY| = |YZ|, calculate the value of m
-
A.
90(^o) -
B.
60(^o) -
C.
45(^o) -
D.
30(^o)
Correct Answer: Option B
Explanation
In the diagram, < WOZ = 180(^o) (angle on a straight line)
< WOX = < XOY = < YOZ
(|WX| = |XY| = |YZ|)
(frac{180^o}{3}) = 60(^o)
= 60(^o)
M + m =2m (base angles of isosceles (bigtriangleup), |OY| and |OZ| are radii)
< YOZ + 2m (base angles of a (bigtriangleup))
60(^o) + 2m = 180(^o) (sum of a (bigtriangleup))
60(^o) + 2m = 180(^o)
2m = 180(^o) – 60(^o)
2m = 120(^o)
m = (frac{120^o}{2})
= 60(^o)