Chapter 11, Problem 8CR

To determine

To find: The Value of $x$ .

Answer to Problem 8CR

Value of $x$ is ${45}^0$ and the triangle is Right angled Isosceles

Explanation of Solution

Given information:

Two angles of a triangle are ${90}^0$ and ${45}^0$

  $x$ is the third angle.

We know

Sum of angles of a triangle is ${180}^0$

Using that

We get

  $\begin{array}{l}x+{90}^0+{45}^0={180}^0\\ \Rightarrow x+{135}^0={180}^0\\ \Rightarrow x+{135}^0-{135}^0={180}^0-{135}^0\\ \Rightarrow x={180}^0-{135}^0\\ \Rightarrow x={45}^0\end{array}$

The triangle has no Obtuse angle

Th triangle has two congruent sides and a Right angle.

So, the triangle is Right angled Isosceles.

Therefore,

Value of $x$ is ${45}^0$ and the triangle is Right angled Isosceles