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Maths-

General

Easy

Question

In $straight triangle XYZ comma straight angle YXZ equals 62 to the power of ring operator text and end text straight angle XYZ equals 54 to the power of ring operator$ and $straight angle XYZ equals 54 to the power of ring operator$ . If YO and ZO are bisectors of $straight angle X Y Z$ and $straight angle X Z Y$ respectively, find $straight angle OZY$ and $straight angle YOZ$ .

hint Hint:

As we know OY and OZ are angular bisectors we find ∠OYZ and ∠OZY.
We find the value of ∠YOZ by using the sum of angles in the triangle is 180°.

The correct answer is: ∠ YOZ = 121°

Step 1:- Find ∠ OYZ and ∠ OZY
given In $straight capital delta$ XYZ
∠YXZ =62° ; ∠ XYZ =54°
We get ∠ YXZ + ∠ XYZ + ∠ XZY =180° (sum of angles in triangle)
∠ XZY = 180-(54 + 62) =180-116 = 64 °
∠ OYZ = $1 half$ ∠ Y(OY is the angular bisector)
∠ OYZ = $1 half$ × 54 = 27°(given ,∠ XYZ =54°)
∠ OZY = $1 half$ ∠ Z (OZ is the angular bisector)
∠ OZY = $1 half$ × 64 = 32°(we got ,∠XZY =64°)
∴ ∠ OZY = 32°
Step 2:- Find ∠YOZ
∠YOZ + ∠OYZ + ∠OZY =180° (sum of angles in triangle OBC)
∠YOZ + 27°+ 32°= 180°
∠YOZ= 180°-59° =121°
∴ ∠YOZ =121°

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