Question 221122: If the complement of an angle is 5 degrees less than one-sixth of its supplement, find the measure of the angle. Answer by drj(1380) (Show Source):
You can put this solution on YOUR website! If the complement of an angle is 5 degrees less than one-sixth of its supplement, find the measure of the angle.
Step 1. Supplementary angles means two angles add up to 180 degrees.
Step 2. Complementary angles means two angles add up to 90 degrees.
Step 3. Let a be the angle.
Step 4. Let 180-a be the supplement of the angle a.
Step 5. Let 90-a be the complement of the angle a.
Step 6. Then since the complement of an angle is 5 degrees less than one-sixth of its supplement, find the measure of the angle.
Step 7. Simplifying Step 6 yields the following steps:
Multiply by 6 to both sides of the equation to get rid of denominator
Add 6a-150 to both sides of the equation to get variable a in left side and numbers on right side.
.
Divide 5 to both sides of the equation
and
Check if equation in Step 6 is true... or which is a true statement.
Step 7. ANSWER: Angle is 78 degrees, its supplementary angle is 102 degrees, and its complementary angle is 12 degrees
I hope the above steps and explanation were helpful.
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