Question

The angles of a right-angled isosceles triangle are
$\begin{array}{l}
A.{90^ \circ },{30^ \circ },{60^ \circ }\\
B.{90^ \circ },{20^ \circ },{70^ \circ }\\
C.{90^ \circ },{40^ \circ },{50^ \circ }\\
D.{90^ \circ },{45^ \circ },{45^ \circ }
\end{array}$

Answer 1

Hint:
Here we apply the concept of triangles.
Sum of angles in a triangle
Property of Isosceles triangle

Complete step by step solution:
The triangle is a right-angled isosceles triangle. Implies one angle is ${90^ \circ }$ and other two acute angles are equal
Let the angles of the triangle be ${90^ \circ }$, $x$ and $x$ respectively.
We know that sum of the angles in a triangle is ${180^ \circ }$
$\begin{array}{l}
 \Rightarrow {90^ \circ } + x + x = {180^ \circ }\\
 \Rightarrow 2x = {180^ \circ } - {90^ \circ }\\
 \Rightarrow 2x = {90^ \circ }\\
 \Rightarrow x = {45^ \circ }
\end{array}$
Therefore the angles in a right angled isosceles triangle are ${90^ \circ }$, ${45^ \circ }$ and ${45^ \circ }$
Hence, Option D is the correct answer.

Note:
In such types of questions which involve the concept of triangles, having knowledge about types of triangles and properties of the triangles is required. By applying the concepts, the required answer is obtained.