Question

The bisectors of the base angles of an isosceles triangle ABC, with AB = AC, meet at O.

If $\angle B=\angle C={50}^{\circ }$. What is the measure of angle O ?

• A. 80^o
• B. 150^o
• C. 130^o
• D. 120^o

Answer 1

fThe correct option is C. ${130}^{\circ }$

$\angle ABC=\angle ACB={50}^{\circ }$ [Angles opposite to equal sides are equal]

$\therefore \angle OBC=\angle OCB=\frac{{50}^{\circ }}{2}={25}^{\circ }$ (Since, OB,OC are bisectors.)

By angle sum property in $\Delta OBC$

$\Rightarrow \angle BOC+{25}^{\circ }+{25}^{\circ }={180}^{\circ }$

$\Rightarrow \angle BOC={180}^{\circ }-{50}^{\circ }$

$\Rightarrow \angle BOC={130}^{\circ }$