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svet-max [94.6K]
3 years ago
5

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 t

he measures of the angles is 195° What is the measure of each angle in degrees ?
Mathematics
1 answer:
hammer [34]3 years ago
6 0

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

<em><u>Solution:</u></em>

Let "x" be the number

<em><u>The measure of one angle is eleven more than four times a number</u></em>

Measure of first angle = 11 + 4(x)

Measure of first angle = 11 + 4x

<em><u>Another angle is twice the first angle’s measure</u></em>

Measure of second angle = twice the measure of first angle

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

<em><u>The sum of the measures of the angles is 195 degrees</u></em>

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

<em><u>Thus, measures of each angle are:</u></em>

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

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