Chapter SH, Problem 10.3.9EP

To determine

The measure of each angle of a triangle is to be determined.

Answer to Problem 10.3.9EP

The measure of each angle of a triangle is $5^{\circ },{45}^{\circ },{130}^{\circ }$

Explanation of Solution

Given:

All the angles of a triangle are in ratio $1:9:26$

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,

  $\begin{array}{l}1x+9x+26x=180\\ \\ 36x=180\\ x=\frac{180}{36}\end{array}$

  $x=5^{\circ }$

Substitute the value of $x=5$ to find the other two angles.

  $\begin{array}{l}9x=9\times 5={45}^{\circ }\\ 26x=26\times 5={130}^{\circ }\end{array}$

Conclusion:

Hence, the measure of each angle of a triangle is $5^{\circ },{45}^{\circ },{130}^{\circ }$