The measure of one angle is eleven more than four times a number. Another angle is twice the first angle's measure. The sum of the measures of the angles is 195° What is the measure of each angle in degrees?

The measure of first angle is 65 degrees and measure of second angle is 130 degrees

Solution:

Let "x" be the number

The measure of one angle is eleven more than four times a number

Measure of first angle = 11 + 4 (x)

Measure of first angle = 11 + 4x

Another angle is twice the first angle's measure

Measure of second angle = twice the measure of first angle

Measure of second angle = 2 (11 + 4x)

The sum of the measures of the angles is 195 degrees

Measure of first angle + Measure of second angle = 195

11 + 4x + 2 (11 + 4x) = 195

11 + 4x + 22 + 8x = 195

12x + 33 = 195

12x = 195 - 33

12x = 162

x = 13.5

Thus, measures of each angle are:

Measure of first angle = 11 + 4x = 11 + 4 (13.5) = 11 + 54 = 65

Measure of second angle = 2 (11 + 4x) = 2 (11 + 4 (13.5)) = 130

Thus measure of first angle is 65 degrees and measure of second angle is 130 degrees