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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