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

Asked on by etyler09

1 Answer | Add Yours

degeneratecircle's profile pic

degeneratecircle | High School Teacher | (Level 2) Associate Educator

Posted on

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.

We’ve answered 319,864 questions. We can answer yours, too.

Ask a question