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22 June, 10:31

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?

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  1. 22 June, 13:31
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    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
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