Question

The base angles of a right angled isosceles triangle measures ___

• A. ${30}^o$
• B. ${45}^o$
• C. ${90}^o$
• D. ${50}^o$

Answer 1

The correct option is B ${45}^o$

In a right angled isosceles triangle, one angle is ${90}^o$ and the other two angles are equal.

Given, $\angle A$ = ${90}^{\circ }$
let the other two angles be $x$ i.e., $\angle B=\angle C=x$

By angle sum property, $\angle A+\angle B+\angle C={180}^{\circ }$

So, ${90}^{\circ }+x+x={180}^{\circ }$

${90}^{\circ }+2x={180}^{\circ }$

$2x={180}^{\circ }-{90}^{\circ }$

$x=\frac{90}{2}$

$x={45}^{\circ }$

Hence the base angles = ${45}^{\circ }$