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