Question

In a triangle two angles are equal and third angle is ${90}^{\circ }$, find the measure of equal angles?

• A. ${45}^{\circ }$
• B. ${60}^{\circ }$
• C. ${90}^{\circ }$
• D. ${30}^{\circ }$

Answer 1

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


Let in $\Delta ABC$ equal angles are$\angle A\text{and}\angle C$.
$\angle A=\angle C$ and $\angle B={90}^{\circ }$

$\angle A+\angle B+\angle C={180}^{\circ }$
[Angle Sum Property]
$\Rightarrow \angle A+\angle B+\angle A={180}^{\circ }$
$\Rightarrow \angle A+{90}^{\circ }+\angle A={180}^{\circ }$
$\Rightarrow 2\angle A={180}^{\circ }-{90}^{\circ }$
$\Rightarrow 2\angle A={90}^{\circ }$
$\Rightarrow \angle A=\frac{{90}^{\circ }}{2}={45}^{\circ }$

$\therefore$ $\angle A=\angle C={45}^{\circ }$.