Question

Question 107

The measure of three angles of a triangle are in the ratio 5 : 3 : 1. Find the measures of these angles.

Answer 1

Let measures of the given angles of a triangle be 5x, 3x and x.
$\because$ Sum of all the angles in a triangle $={180}^{\circ }$
$\therefore 5x+3x+x={180}^{\circ }\Rightarrow 9x={180}^{\circ }\Rightarrow x=\frac{{180}^{\circ }}{9}\Rightarrow x={20}^{\circ }$
So, the angles are $5x=5\times {20}^{\circ }={100}^{\circ },3x=3\times {20}^{\circ }={60}^{\circ }$ and $x={20}^{\circ }$ i.e. ${100}^{\circ },{60}^{\circ }$ and ${20}^{\circ }$