JAMB 1995 · UME · Q28

Angles, triangles & polygons

In a triangle $XYZ$ , $\angle YXZ = 44^\circ$ and $\angle XYZ = 112^\circ$ . Calculate the acute angle between the internal bisectors of $\angle XYZ$ and $\angle XZY$ .

Worked solution (try it first)

The angles of triangle $XYZ$ add up to $180^\circ$ : $\angle XZY = 180^\circ - 44^\circ - 112^\circ$
$= 24^\circ$ .
The bisectors make $112^\circ \div 2 = 56^\circ$ and $24^\circ \div 2 = 12^\circ$ with $YZ$ .
In the triangle they form with $YZ$ , the angle where they meet is $180^\circ - 56^\circ - 12^\circ = 112^\circ$ .
The acute angle between the lines is $180^\circ - 112^\circ = 68^\circ$ , option C.

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