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Question 158957: Please help me solve this problem, it is from a worksheet:
the measure of angle b, the complement of angle a is 1/6th the measure of angle c, the supplement of angle a Find the measure of each angle
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! the measure of angle b, the complement of angle a is 1/6th the measure of angle c, the supplement of angle a Find the measure of each angle
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The problem expects you to know that:
If two angles are complementary, the sum of their angles equals 90 deg.
If two angles are supplementary, the sum of their angles equals 180 deg.
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Let a = angle
then
90-a = complement of the angle (angle b)
180-a = supplement of the angle a (angle c)
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Then from: "the measure of angle b, the complement of angle a is 1/6th the measure of angle c, the supplement of angle a" we get our equation of:
90-a = (1/6)(180-a)
multiplying both sides by 6:
540-6a = 180-a
540 = 180+5a
360 = 5a
72 degrees = a (angle a)
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Angle b:
90-a = 90-72 = 18 degrees (angle b)
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Angle c"
180-a = 180-72 = 108 degrees (angle c)
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