Question

In the figure below if AB $=$ AC, the value of x is :

• A. ${55}^{\circ }$
• B. ${110}^{\circ }$
• C. ${50}^{\circ }$
• D. ${70}^{\circ }$

Answer 1

The correct option is D ${70}^{\circ }$

$AB=AC$

$\Rightarrow \angle B=\angle C$ (As angles opposite to equal sides are equal)

Let each be $y$

Now in $△ABC$ by using angle sum proerty of triangle

$\angle A+\angle B+\angle C={180}^{\circ }x+y+y={180}^{\circ }\Rightarrow x+2y={180}^{\circ }..............\left(i\right)$

Also

$\angle ABC+{125}^{\circ }={180}^{\circ }$ (Supplementary angles)

$\Rightarrow y+{125}^{\circ }={180}^{\circ }..........\left(ii\right)$

Slolving $\left(i\right)$ and $\left(ii\right)$

$\Rightarrow x={70}^{\circ },y={55}^{\circ }$