The supplement of an angle is six times as large as the complement of the angle .what is the measure of the angle to the nearest whole degrees

The angle measures 72°

Step-by-step explanation:

Convert the given statements into equations.

*Know that complementary angles add up to 90° and supplementary angles add up to 180°

"The supplement of an angle is six times as large as the complement of the angle" becomes

180° - a  = 6(90° - a)          

 **180° - a is the supplement.    If angle + supplement = 180°, then

         180° - angle = supplement

 **90° - a is the complement.    If angle + complement = 90°, then

         180° - angle = complement

Now solve the equation         180° - a  = 6(90° - a)    

   180° - a = 540° - 6a              (distribute the 6 on the right side)

            6a - a = 540° - 180°      (bring variables to one side, and constants

                                                     to the other)

            5a = 360°                    (simply both sides)

                  a = 72°                  (Solve for a by dividing both sides by 5)

***This makes the complement 18° (72 + 18 = 90)

and the supplement 108° (72 + 108 = 180).  We can see that 108 = 6(18) so we have the right answer!

5

Step-by-step explanation: