SOLUTION: Two angles are complementary. The measure of the larger is 6 less than 3 times the measure of the smaller. Find the measure of both angles. Two angles are supplementary. The

Algebra ->  Angles -> SOLUTION: Two angles are complementary. The measure of the larger is 6 less than 3 times the measure of the smaller. Find the measure of both angles. Two angles are supplementary. The       Log On


   

Question 163841: Two angles are complementary. The measure of the larger is 6 less than 3 times the measure of the smaller. Find the measure of both angles.
Two angles are supplementary. The measure of the larger is 54 more than 8 times the measure of the smaller. Find the measure of both angles
Answer by midwood_trail(310) About Me  (Show Source):
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Two angles are complementary. The measure of the larger is 6 less than 3 times the measure of the smaller. Find the measure of both angles.
If two angles are complementary, they add up to 90 degrees.
x + x = 90
larger angle = 3x - 6
smaller angle = x
Set up the equation and solve for x.
x + 3x - 6 = 90
4x - 6 = 90
4x = 90 + 6
4x = 96
x = 96/4
x = 24
larger angle = 3(x) - 6
larger angle = 3(24) - 6
larger angle = 72 - 6
larger angle = 66 degrees
smaller angle = x = 24 degrees
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Two angles are supplementary. The measure of the larger is 54 more than 8 times the measure of the smaller. Find the measure of both angles.
If two angles are supplementary, they add up to 180 degrees.
x + x = 180
larger angle = 8x + 54
smaller angle = x
8x + 54 + x = 180
9x + 54 = 180
9x = 180 - 54
9x = 126
x = 126/9
x = 14
The smaller angle = 14 degrees
larger angle = 8x + 54
larger angle = 8(14) + 54
larger angle = 112 + 54
larger angle = 166 degrees
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