Question

Determine the measure of each of the equal angles of a right-angled isosceles triangle

OR

ABC is a right-angled triangle in which $\angle A={90}^{\circ }andAB=AC.Find\angle Band\angle C.$

Answer 1

Given : In a right angled isosceles $\Delta ABC,$

$\angle A={90}^{\circ }andAB=AC$

To determine, each equal angle of the triangle

$\because \angle A={90}^{\circ }\therefore \angle B+\angle C={90}^{\circ }But\angle B=\angle C\therefore \angle B+\angle B={90}^{\circ }\Rightarrow 2\angle B={90}^{\circ }\Rightarrow \angle B=\frac{{90}^{\circ }}{2}={45}^{\circ }and\angle C=\angle B={45}^{\circ }Hence\angle B=\angle C={45}^{\circ }$