# A supplement of an angle is 6 times as large as the complement of the angle. Find the measure of the angle.

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Expert Answers

degeneratecircle | Certified Educator

Call the measure of the angle `x`. The supplement of the angle `x` is the angle `y` such that `x+y=180`` `. If we solve for `y` by subtracting `x` from both sides ,we see that the supplement of `x` is `180-x` (and we can check that if we add `x` and `180-x`, we do get 180).

If we use the same exact reasoning, using 90 instead of 180, we see that the complement of `x` is `90-x`.

Since the supplement is 6 times as large as the complement, this gives us the equation `180-x=6(90-x)`. Distribute the 6 on the right side to get

`180-x=540-6x`. Now it's just a matter of solving for `x`. If we get the `x` terms on one side we have `5x=360`, or `x=72` degrees.

**The answer is 72` ` degrees**.