Question : In a $\triangle ABC$, the bisectors of $\angle$ABC and $\angle$ACB intersect each other at point O. If the $\angle$BOC is 125°, then the $\angle$BAC is equal to:
Option 1: 75°
Option 2: 78°
Option 3: 70°
Option 4: 82°
Correct Answer: 70°
Solution : Given: $\angle$BOC $=\ 125^\circ$ BO and OC is angle bisector. Now, By angle bisector theorem $\Rightarrow \angle BOC\ =\ 90^\circ\ +\ \frac{1}{2}\angle BAC$ $\Rightarrow 125^\circ\ =\ 90^\circ\ +\ \frac{1}{2}\angle BAC$ $\Rightarrow \angle BAC\ =\ 70^\circ$ Hence, the correct answer is 70°
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Question : In $\triangle$ABC, $\angle$A = 66°. AB and AC are produced at points D and E, respectively. If the bisectors of $\angle$CBD and $\angle$BCE meet at the point O, then $\angle$BOC is equal to:
Question : Internal bisectors of $\angle$ B and $\angle$ C of $\triangle$ ABC meet at O. If $\angle$ BAC = $80^{\circ}$, then the value of $\angle$ BOC is:
Question : In $\triangle A B C $, AB and AC are produced to points D and E, respectively. If the bisectors of $\angle C B D$ and $\angle B C E$ meet at the point O, and $\angle B O C=57^{\circ}$, then $\angle A$ is equal to:
Question : In a triangle, ABC, BC is produced to D so that CD = AC. If $\angle BAD=111^{\circ}$ and $\angle ACB=80^{\circ}$, then the measure of $\angle ABC$ is:
Question : Two angles of a triangle are equal and the third angle measures 70°. What is the measure of each of the unknown angles?
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