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Maths-

General

Easy

Question

In figure $angle X equals 62 to the power of ring operator end exponent comma angle X Y Z equals 54 to the power of ring operator end exponent$ If YO and ZO are bisectors of $angle X Y Z$ and $angle X Z Y$ respectively of $capital delta X Y Z$ , find $angle Y O Z$

$71^{\circ}$
$32^{\circ}$
$55^{\circ}$
${121 S}^{\circ}$

hint Hint:

The correct answer is: $121 S to the power of ring operator end exponent$

We should find ∠YOZ
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

Hence choice 4 is correct

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