Question : In $\triangle \mathrm{XYZ}$, I is the incentre of the $\triangle \mathrm{XYZ}$. If $\angle \mathrm{XYZ}=40$$^\circ$, then what is the value of $\angle \mathrm{XIZ}$?
Option 1: 110$^\circ$
Option 2: 130$^\circ$
Option 3: 115$^\circ$
Option 4: 120$^\circ$
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Correct Answer: 110$^\circ$
Solution :
Given, I is the incentre of the $\triangle \mathrm{XYZ}$.
$\angle \mathrm{XYZ}=40^\circ$
Since angle formed at incentre opposite to any side of triangle = $90^\circ+\frac{1}{2}\times$ (Angle opposite to that side of triangle)
So, $\angle \mathrm{XIZ} = 90^\circ+\frac{1}{2}\times \angle \mathrm{XYZ}$
= $90^\circ+\frac{1}{2}\times 40^\circ$
= $90^\circ+20^\circ$
= $110^\circ$
Hence, the correct answer is 110$^\circ$.
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