Question

The angles in a right-angled isosceles triangle are

• A. $90°,45°,45°$
• B. $90°,30°,60°$
• C. $90°,20°,70°$
• D. none of these

Answer 1

The correct option is A

$90°,45°,45°$

An isosceles triangle base angles are equal.

In a right-angled isosceles triangle, one angle is $90°$.

Let the other two angles be $x$

We know, Sum of all angles of a triangle is $180°$

$$\begin{gathered} \Rightarrow 90°+x+x=180° \\ \Rightarrow 90+2x=180 \\ \Rightarrow 2x=180-90 \\ \Rightarrow 2x=90 \\ \Rightarrow x=\frac{90}{2} \\ \Rightarrow x=45° \end{gathered}$$

Therefore, the other two angles will be $45°$each.

So, the angles are $90°,45°,45°$

Hence option A is correct.