SOLUTION: Two angles are supplementary if the sum of their measures is 180°. The measure of the first angle is 36° less than three times the second angle.
What is the measure of the small
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What is the measure of the small
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Question 1124825: Two angles are supplementary if the sum of their measures is 180°. The measure of the first angle is 36° less than three times the second angle.
What is the measure of the smaller of the two angles?
A. The smaller angle has a measure of 54 degrees.
B. The smaller angle has a measure of 108 degrees.
C. The smaller angle has a measure of 26 degrees.
D. The smaller angle has a measure of 72 degrees Answer by Theo(13342) (Show Source):
the sum of the measure of both angles is 180 degrees.
let x = the measure of the second angle.
the measure of the second angle is 3 * x - 36.
the sum of the angles = 180 becomes x + 3 * x - 36 = 180
add 36 to both sides of this equation to get x + 3 * x = 216
combine like terms to get 4x = 216
solve for x to get x = 216 / 4 = 54.
that's the measure of the second angle.
the measure of the first angle is 3 * 54 - 36 = 162 - 36 = 126.
the first angle is 126.
the second angle is 54.
the sum of the angles is 126 + 54 = 180
the first angle is 36 less than 3 * the second angle becomes 126 = 3 * 54 - 36 which becomes 162 - 36 = 126 which becomes 126 = 126.
solution is confirmed to be good.
solution is the measure of the smaller angle is 54 degrees.
