# In Fig. 6.40, ∠X = 62°, ∠XYZ = 54°. If YO and ZO are the bisectors of ∠XYZ and ∠XZY respectively of △XYZ, find ∠OZY and ∠YOZ.

**Solution:**

Given: ∠X = 62°, ∠XYZ = 54°, and YO and ZO are the bisectors of ∠XYZ and ∠XZY respectively.

To find: ∠OZY and ∠YOZ

According to the angle sum property of a triangle, sum of the interior angles of a triangle is 180°.

Consider △XYZ

∠X + ∠XYZ + ∠Z = 180° [Angle sum property of a triangle]

62° + 54° + ∠Z = 180°

∠Z = 180° - 116°

∠Z = 64°

Now, OZ is the angle bisector of ∠XZY

Thus, ∠OZY = (1/2) of ∠XZY = 1/2 × 64° = 32° ..........(i)

Similarly, OY is the angle bisector of ∠XYZ

Thus, ∠OYZ = (1/2) of ∠XYZ = 1/2 × 54° = 27°......... (ii)

Now, in △OYZ

∠OYZ + ∠OZY + ∠YOZ = 180° [Angle sum property of a triangle]

27° + 32° + ∠YOZ = 180° [from (i) and (ii)]

∠YOZ = 180° - 59°

∠YOZ = 121°

Hence, ∠OZY = 32° and ∠YOZ = 121°

**Video Solution:**

## In Fig. 6.40, ∠X = 62°, ∠XYZ = 54°. If YO and ZO are the bisectors of ∠XYZ and ∠XZY respectively of △XYZ, find ∠OZY and ∠YOZ

### NCERT Maths Solutions Class 9 - Chapter 6 Exercise 6.3 Question 2:

**Summary:**

In Fig. 6.40, if ∠X = 62°, ∠XYZ = 54°, and YO and ZO are the bisectors of ∠XYZ and ∠XZY respectively of ΔXYZ, then ∠OZY = 32°, and ∠YOZ = 121°.