Question

ABC is a right-angled triangle in which $\angle A={90}^{\circ }$ and AB = AC. Then, $\angle B$ equals

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

Answer 1

Answer: (B), (D)

$\angle C$

It is given that AB = AC.
$\Rightarrow \angle C=\angle B$
(Angles opposite to equal sides of a triangle are equal.)


In $\Delta ABC$,
$\angle A+\angle B+\angle C={180}^{\circ }$
(Angle sum property of a triangle)
$\Rightarrow {90}^{\circ }+\angle B+\angle C={180}^{\circ }\Rightarrow {90}^{\circ }+\angle B+\angle B={180}^{\circ }\Rightarrow 2\angle B={90}^{\circ }\Rightarrow \angle B={45}^{\circ }\therefore \angle B=\angle C={45}^{\circ }$