In the diagram, \(\bar{OX}\) bisects < YXZ and \(\bar{OZ}\) bisects < YZX. If < XYZ...

WAEC 2015

In the diagram, \(\bar{OX}\) bisects < YXZ and \(\bar{OZ}\) bisects < YZX. If < XYZ = 68^o, calculate the value of < XOZ

A. 68^o
B. 72^o
C. 112^o
D. 124^o

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Correct Answer: Option D

Explanation

In \(\Delta\) XYZ, 2m + 2n + 68^o = 180^o

2(m + n) + 68^o = 180^o...(1)

in \(\Delta\) XOZ, m + n + q = 180^o ...(2)

(m + n) = 180^o - q...(3)

substituting 180^o - q for (m + n) in (1) gives

2(180^o - q) + 68^o = 180^o

360^o - 2q = 180^o - 68^o

360^o - 2q = 112^o

360^o - 112^o = 2q

248^o = 2q

q = \(\frac{248^o}{2}\)

= 124^o

hence, < XOZ = 124^o

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