Question

In the adjoining figure, XY = XZ. YQ and ZP are the bisectors
of ZXYZ and ZXZY respectively. Prove that YQ = ZP.
P
Z​

Answer 1

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MATHS

In given figure ∠X=62

∘

,∠XYZ=54

∘

. If YO and ZO are the bisectors of ∠XYZ and ∠XZY respectively of ΔXYZ . find ∠OZY and ∠YOZ .

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ANSWER

As the sum of all interior angles of a triangle is 180º, therefore, for ΔXYZ,

∠X + ∠XYZ + ∠XZY = 180º

62º + 54º + ∠XZY = 180º

∠XZY = 180º − 116º

∠XZY = 64º

∠OZY = 32º (OZ is the angle bisector of ∠XZY)

Similarly, ∠OYZ == 27º

Using angle sum property for ΔOYZ, we obtain

∠OYZ + ∠YOZ + ∠OZY = 180º

27º + ∠YOZ + 32º = 180º

∠YOZ = 180º − 59º

∠YOZ = 121º

Step-by-step explanation:

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