Question

In the given 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.

Answer 1

Answer:

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

Answer 2

Answer:

angle OYZ = 27 degree

angle OZY=33 degree (angle sum property of big triangle and angle bisector of small triangle)

hence by angle sum property

angle YOZ = 180-33+27

=180-60

=120 degree

Step-by-step explanation:

hope it helps

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