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In the following figure, angle X=62°, angle XYZ=54°. If YO and ZO are the bisectors of angle XYZ and angle XZY respectively of triangle XYZ, find angle OZY and angle YOZ. |
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Answer» As the SUM of all interior ANGLES of a triangle is 180º, therefore, for ΔXYZ,∠X + ∠XYZ + ∠XZY = 180º62º + 54º + ∠XZY = 180º∠XZY = 180º − 116º∠XZY = 64º∠OZY = 32º (OZ is the angle bisector of ∠XZY)Similarly, ∠OYZ == 27ºUsing angle sum PROPERTY for ΔOYZ, we obtain∠OYZ + ∠YOZ + ∠OZY = 180º27º + ∠YOZ + 32º = 180º∠YOZ = 180º − 59º∠YOZ = 121º |
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