Find the measures of the angles of the triangle if one of them is 2 times larger than the second

Find the measures of the angles of the triangle if one of them is 2 times larger than the second and 3 times smaller than the third.

This problem will be solved using the equation;

Let x be the measure of the second angle;

Then 2 * x is the measure of the first angle;

3 * 2 * x – degrees measure of the third angle;

We also know that the sum of all angles in a triangle is 180 °, we make an equation of the following form:

x + 2 * x + 3 * 2 * x = 180 °;

x + 2 * x + 6 * x = 180 °;

9 * x = 180 °;

x = 180 °: 9;

x = 20 °.

20 ° is the measure of the second angle;

2 * 20 ° = 40 ° – measure of the first angle;

3 * 40 ° = 120 ° is the measure of the third angle.

Answer: 40 ° is the measure of the first angle; 20 ° is the measure of the second angle; 120 ° is the measure of the third angle.