Question

In figure, _X = 62°, ZXYZ = 54º. If YO and ZO
are the bisectors of ZXYZ and ZXZY respectively
of AXYZ, find ZOZY and ZYOZ.​

Answer 1

Step-by-step explanation:

here your answer.

xzy = 64

then

64÷2=32

ozy= 32

Last

yoz+27+32=180

yoz+59=180

yoz=180-59

yoz=21

Full on top

Answer 2

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Given:-

• OY is the Angle bisector of ∠XYZ

So,

$∠XYO= ∠OYZ= \frac{1}{2}(∠XYZ)$

$= > ∠XYO= ∠OYZ= \frac{1}{2}(54\degree)$

$= > ∠XYO= ∠OYZ= 27\degree. \: . \: .(1)$

Also,

• OZ is the Angle bisector of ∠XZY

So,

$∠XZO= ∠OZY= \frac{1}{2}(∠XZY). \: . \: .(2)$

$In \: \triangle XYZ$

$∠YXZ+∠XYZ+∠XZY=180°$

$= > 62\degree + 54\degree∠XZY=180°$

$= > ∠XZY=180° - 116\degree$

$= > ∠XZY=64\degree$

From Equation (2),

$= > ∠XZO= ∠OZY= \frac{1}{2}(∠XZY)$

$= > ∠XZO= ∠OZY= \frac{1}{2}(64\degree)$

$= > ∠XZO= ∠OZY= 32\degree$

Now,

$In \: \triangle \: OYZ$

$∠OYZ+∠OZY+∠YOZ=180° \\ = > 27\degree + 32\degree + ∠YOZ=180°$

$= > 59\degree \: + ∠YOZ=180°$

$= > ∠YOZ=180° - 59\degree$

$= > YOZ=121\degree$