SOLUTION: the measure of the supplement of an angle is 6 times the measure of its complement. Find the angle measure

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Question 1131250: the measure of the supplement of an angle is 6 times the measure of its complement. Find the angle measure
Found 3 solutions by ikleyn, josmiceli, greenestamps:
Answer by ikleyn(52781) About Me  (Show Source):
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.
Let x be the angle measure in degrees.


Then the supplementary angle is (180-x) degrees, while the complementary angle is (90-x) degrees.


Then the problem says


180-x = 6*(90-x)


180 - x = 540 - 6x


6x - x = 540 - 180


5x = 360


x = 360%2F5 = 72 degrees.     Answer


Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +theta+ = the unknown angle
+180+-+theta+ = the supplement
+90+-+theta+ = the complement
--------------------------------------------
+180+-+theta+=+6%2A%28+90+-+theta+%29+
+180+-+theta+=+540+-+6%2Atheta+
+5%2Atheta+=+540+-+180+
+5%2Atheta+=+360+
+theta+=+72+ degrees

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The supplement of an angle is 90 degrees more than the complement of the same angle. Since we are told that the supplement is 6 times the complement, if x is the measure of the complement then

6x+=+90%2Bx
5x+=+90
x+=+18

The complement of the angle is 18 degrees; so the angle is 90-18 = 72 degrees.