Question

The angles in a right angled isosceles triangle are:

• A. ${60}^o,{60}^o,{60}^o$
• B. ${90}^o,{60}^o,{30}^o$
• C. ${90}^o,{45}^o,{45}^o$
• D. ${70}^o,{50}^o,{60}^o$

Answer 1

Answer: (C)

${90}^o,{45}^o,{45}^o$

Let the triangle is right angles at $C$ with $AC=BC$

$\Rightarrow \angle B=\angle C$ (Angles opposite to equal side are equal)

Using angle sum property of triangle in $△ABC$

$\angle A+\angle B+\angle C={180}^{\circ }$

Now $\angle C={90}^{\circ }$ and $\angle A=\angle B$

$\Rightarrow {\angle A+\angle A+90}^{\circ }={180}^{\circ }\Rightarrow 2\angle A={90}^{\circ }\Rightarrow \angle A={45}^{\circ }$

So the angles are ${90}^{\circ },{45}^{\circ },{45}^{\circ }$