Chapter SH, Problem 10.3.7EP

To determine

The measure of each angle of a triangle.

Answer to Problem 10.3.7EP

The measure of each angle of a triangle is ${30}^{\circ }$ , ${60}^{\circ }$ , ${90}^{\circ }$ .

Explanation of Solution

Given:

All the angles of a triangle are in ratio $1:2:3$

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.

Now the equation is written as,

  $x+2x+3x=180$

  $6x=180$

  $x=\frac{180}{6}$

  $x=30$

Substitute the value of $x=30$ to find the other two angles.

  $\begin{array}{l}2x=2\times 30={60}^{\circ }\\ 3x=3\times 30={90}^{\circ }\end{array}$

Conclusion:

Hence, the measure of each angle of a triangle is ${30}^{\circ }$ , ${60}^{\circ }$ , ${90}^{\circ }$ .