Question

For a triangle $ABC$, right - angled at $B$, if $m\angle A=m\angle B$, then $m\angle A=$

• A. ${45}^{\circ }$
• B. ${50}^{\circ }$
• C. ${55}^{\circ }$

Answer 1

The correct option is A ${45}^{\circ }$

Given for $△ABC$, $m\angle A=m\angle C$ and $m\angle B={90}^{\circ }$
Now, according to the angle sum property of the triangle:
$m\angle A+m\angle B+m\angle C={180}^{\circ }$
$\Rightarrow m\angle A+{90}^{\circ }+m\angle A={180}^{\circ }$
$\Rightarrow 2\times m\angle A={180}^{\circ }-{90}^{\circ }$
$\Rightarrow 2\times m\angle A={90}^{\circ }$
$\Rightarrow m\angle A={90}^{\circ }\times \frac{1}{2}={45}^{\circ }$
$\Rightarrow m\angle A={45}^{\circ }$