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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

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 $^o$

View answer & explanation

Correct answer is B

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 $^o$

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