Question

In Triangle XYZ, Angle X = 70 Degrees and Angle Y = 60 Degrees. YO and ZO are bisectors of Angle Y and Angle Z intersecting at Point 'O'. Then Angle YOZ is_

Answer 1

Answer:

Your answer ∠YOZ = 125°

Step-by-step explanation:

We know that sum of all the angles in a triangle is 180

So,

= ∠X + ∠Y +∠Z = 180

= 70 + 60 + ∠Z = 180

= 130 + ∠Z = 180

= ∠Z = 180 - 130 = 50

= ∠Z = 50

The given that ZO and YO are the bisectors of ∠Y and ∠Z

So,

= ∠OYZ = ∠OYX = 2∠OYZ = 60

From that we get

= ∠OYZ = 30

same as before for  ∠Z

= 2∠YZO = 50

= ∠YZO = 25

now in ΔOYZ

= ∠OYZ + ∠YZO + ∠YOZ = 180

= 30 + 25 + ∠YOZ = 180

= 55 +∠YOZ = 180

= ∠YOZ = 180 - 55 = 125

= ∠YOZ = 125

Your answer ∠YOZ = 125°

Diagram of the triangle given below please checkout

hope this helps u

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