Question

In ΔXYZ, O is the incentre. If ∠XYZ = 46°, ∠XZY = 54°, then find the measure of ∠YOZ.  

1. 95°
2. 65°
3. 130°
4. 100°

Answer 1

Correct Answer - Option 3 : 130°

Given:

In ΔXYZ, O is the incentre.

∠XYZ = 46°, ∠XZY = 54°

Concepts used:

Sum of all three angles of triangle is 180°.

Angle formed at incentre opposite to given side = 90° +( ½ × angle opposite to given side)

Calculation:

In ΔXYZ, according to sum angle property of triangle

∠X + ∠Y + ∠Z = 180°

⇒ ∠X + 46° + 54° = 180°

⇒ ∠X = 180° - 100°

⇒ ∠X = 80°

In ΔXYZ, O is the incentre.

Angle formed at incentre opposite to given side = 90° +( ½ × angle opposite to given side)

⇒ ∠YOZ = 90° + (1/2 × ∠X)

⇒ ∠YOZ = 90° + (80°/2)

⇒ ∠YOZ = 130°

∴ Measure of ∠YOZ is equal to 130°.