SOLUTION: The supplement of an angle is 60 degrees less than twice the supplement of the complement of the angle. Find the measure of the complement.

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Question 1183528: The supplement of an angle is 60 degrees less than twice the supplement of the complement of the angle. Find the measure of the complement.
Answer by ikleyn(53937) About Me  (Show Source):
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The supplement of an angle is 60 degrees less than twice the supplement of the complement of the angle.
Find the measure of the complement.
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Let x be  the angle  (which is called  "an angle"  in the problem's description).


Then the supplement is  (180-x) degrees,

and the complement is (90-x) degrees, while the supplement of the complement of the angle is  (180 - (90-x)) = 90+x degrees.


Next, write the equation as you read the text


    180-x = 2*(90+x) - 60.


Simplify and find x


    180-x = 180 + 2x - 60

       -x =       2x - 60

       60 =       2x + x

       60 =       3x

        x =       60/3 = 20.


Thus the angle is 20 degrees, and its complement (which is under the problem's question) is 90-20 = 70 degrees.    ANSWER

Solved and explained.

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To see many other similar  (and different)  solved problems on supplementary and complementary angles,  look into the lessons
    - Angles basics
    - Vertical angles
    - HOW TO solve problems on supplementary, complementary or vertical angles - Examples
    - Solved problems on supplementary and complementary angles
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