Chapter SH, Problem 10.3.8EP

To determine

The measure of angles of $\Delta ABC$ .

Answer to Problem 10.3.8EP

The measure of angles of $\Delta ABC$ is ${45}^{\circ },{45}^{\circ },{90}^{\circ }$

Explanation of Solution

Given:

The measures of the angles of a triangle are given in a ratio of $1:1:2$ .

Concept Used:

The sum of all the angles of a triangle is ${180}^{\circ }$ .This statement is valid for all types of triangles.

Calculation:

As the sum of all the angles of a triangle is ${180}^{\circ }$ ,

Consider $x$ as a common ratio.

In $\Delta ABC$ consider,

  $\begin{array}{l}\angle A=1x\\ \angle B=1x\\ \angle C=2x\end{array}$

Now the equation is written as, the measure of all angles of triangle is ${180}^{\circ }$ .

  $\begin{array}{l}1x+1x+2x=180\\ 4x=180\\ x=\frac{180}{4}\\ x={45}^{\circ }\end{array}$

  $\angle A={45}^{\circ }$

Substitute the value of $x={45}^{\circ }$ to find the other two angles.

  $\begin{array}{l}\angle B=1\times 45={45}^{\circ }\\ \angle C=2\times 45={90}^{\circ }\end{array}$

Conclusion:

Hence, the measure of angles of $\Delta ABC$ is ${45}^{\circ },{45}^{\circ },{90}^{\circ }$ .