Question

The measure of one of the angles of a triangle is 5 times the measure of its smallest angle and the measure of the other is thrice the measure of the smallest angle. Find the measures of the three angles.

Answer 1

Let the smallest angle be x.
Then measure of second angle = 2x (Given measure of one angle is twice the smallest angle)
Measure of third angle = 3x.
(Given measure of other angle is thrice the smallest angle)
$x+5x+3x={180}^{\circ }\text{(Angle sum property of a triangle)}$
$9x={180}^{\circ }$
$x=\frac{180}{9}={20}^{\circ }$
$5x=2\times 20={100}^{\circ }$
$3x=3\times 20={60}^{\circ }$
Hence the measures of the angles are ${20}^{\circ },{100}^{\circ }\text{and}{60}^{\circ }.$