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Question

In the given figure, X=62o,XYZ=54o. In XYZ If YO and ZO are the bisectors of XYZ and XZY respectively find OZY and YOZ.
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Solution

In XYZ
XYZ+XZY+YXZ=180 (Angle sum property)

54+XZY+62=180

XZY=180116=64

OZY=12XZY (Given OZ is the angle bisector)

OZY=12×64=32

OYZ=12XYZ (Given OY is then angle bisector)

OYZ=12×54=27
In OYZ
YOZ+OYZ+OZY=180

54+XZY+62=180

YOZ+27+32=180

YOZ=18059=121

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