Question : In $\triangle \mathrm{ABC}, \angle \mathrm{A}=54^{\circ}$. If I is the incentre of the triangle, then the measure of $\angle \mathrm{BIC}$ is:
Option 1: 68o
Option 2: 54o
Option 3: 148o
Option 4: 117o
Answer (1)
24th Jan, 2024
Correct Answer: 117 o
Solution :
In $\triangle ABC$,
$\angle A = 54^{\circ}$
$\angle BIC = 90^{\circ} + \frac{\angle A}{2}$
$= 90^{\circ} + \frac{54^{\circ}}{2}$
$= 90^{\circ} + 27^{\circ}$
$= 117^{\circ}$
Hence, the correct answer is 117º.
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