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WAEC Mathematics 2015 Paper

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Question : 45

Total: 45

In the diagram,

\overline{OX}

bisects < YXZ and

\overline{OZ}

bisects < YZX. If < XYZ = 68^o, calculate the value of < XOZ

68^o
72^o
112^o
124^o

Solution:

Concept:

Use the angle-sum property of triangles along with the fact that the given lines bisect two angles of

\triangle XYZ

.

Explanation:

Let

\angle YXZ = 2m

and

\angle YZX = 2n

.

Since

\overline{OX}

bisects

\angle YXZ

, each part is

m

.

Since

\overline{OZ}

bisects

\angle YZX

, each part is

n

.

In

\triangle XYZ

, the sum of angles is

180^\circ

:

2m + 2n + 68^\circ = 180^\circ

2(m+n) = 180^\circ - 68^\circ

2(m+n) = 112^\circ

m+n = 56^\circ

In

\triangle XOZ

, let

\angle XOZ = q

.

m + n + q = 180^\circ

56^\circ + q = 180^\circ

q = 124^\circ

Answer:

\angle XOZ = 124^\circ

, so the correct option is D:

124^\circ

.

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