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

answer: 180 degrees clockwise

step-by-step explanation:

1st integer x

2nd integer x+1

3rd integer x+2

4th integer x+3

x+x+1 +x+2+x+3 =74

combine like terms

4x+6 = 74

subtract 6 from each side

4x = 68

x = 17

the integers are 17,18,19,20