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\(^o\)
waec 2018mathematics

The correct answer is B. 60\(^o\)

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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