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
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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Question : In $\triangle \mathrm{ABC}, \angle \mathrm{A}=68^{\circ}$. If I is the incentre of the triangle, then the measure of $\angle B I C$ is:
Question : In a $\triangle \mathrm{ABC}$, the bisectors of $\angle \mathrm{B}$ and $\angle \mathrm{C}$ meet at $\mathrm{O}$. If $\angle \mathrm{BOC}=142^{\circ}$, then the measure of $\angle \mathrm{A}$ is:
Question : 'I' is the incentre of $\triangle$ABC. If $\angle$BIC = 108$^\circ$, then $\angle$A = ?
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Question : In $\triangle \mathrm{ABC}, \mathrm{BD} \perp \mathrm{AC}$ at D. E is a point on BC such that $\angle \mathrm{BEA}=x^{\circ}$. If $\angle \mathrm{EAC}=62^{\circ}$ and $\angle \mathrm{EBD}=60^{\circ}$, then the value of $x$ is:
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