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.

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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