in figure angle X is equals to angle 54 angle xyz is equals to 70. if YO and ZO are the bisector andle xyz and angle xzy respectively of triangle xyz find angle ozy and angle yozin figure angle X is equals to angle 54 angle xyz is equals to 70. if YO and ZO are the bisector andle xyz and angle xzy respectively of triangle xyz find angle ozy and angle yoz

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History
Author:
tabetha
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1 year ago

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Answer:

In the given figure, ∠X = 62° and ∠XYZ = 54° ∠XYZ + ∠XZY + ∠YXZ = 180° …(i) [Angle sum property of a triangle] ⇒ 54° + ∠XZY + 62° = 180° ⇒ ∠XZY + 116° = 180° ⇒ ∠XZY = 180° – 116° = 64° Now, ∠OZY = 1/ 2 × ∠XZY [∵ZO is bisector of ∠XZY] = 1 /2 × 64° = 32° Similarly, ∠OYZ = 1/2 × 54° = 27° Now, in ∆OYZ, we have ∠OYZ + ∠OZY + ∠YOZ = 180° Angle sum property of a triangle] ⇒ 27° + 32° + ∠YOZ = 180° ⇒ ∠YOZ = 180° – 59° = 121° Hence, ∠OZY = 32° and ∠YOZ = 121°

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