Question

In a triangle , the measure of the first angle is twice the measure of the second angle. The measure of the third angle is 100 more than the measure of the second angle. Use the fact that the sum of the measures of the three angles of a triangle is 180 to find the measure of each angle .

Answer 1

The three unknown angles X, Y , and Z are:

X = 40, Y = 20, and Z = 120

Explanation:

Let's name X the measure of the first angle, Y the measure of the second one, and Z that of the third one.

Then we can create the following equations:

X = 2 Y

Z = 100 + Y

and

X + Y + Z = 180

So we use the first equation and the second one to substitute for the variable X and Z in the thrid equation:

2 Y + Y + (100 + Y) = 180

4 Y + 100 = 180

4 Y = 80

Y = 80/4 = 20

Then X = 40, Y = 20, and Z = 120