Question : I is the incentre of the $\triangle$XYZ. If $\angle$YIZ = 115°, then what is the $\angle$YXZ?
Option 1: 55°
Option 2: 45°
Option 3: 50°
Option 4: 60°
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Correct Answer: 50°
Solution :
In $\triangle$XYZ, I is the incentre.
Angle formed at incentre opposite to given side = 90° + ($\frac{1}{2}$ × Angle opposite to given side)
⇒ $\angle$YIZ = 90° + ($\frac{1}{2}$ × $\angle$YXZ)
⇒ 115° = 90° + ($\frac{1}{2}$ × $\angle$YXZ)
⇒ $\frac{1}{2}$ × $\angle$YXZ = 25°
⇒ $\angle$YXZ = 50°
Hence, the correct answer is 50°.
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