The measure of the supplement of an angle is 10 more than twice the measure of the complement of the angle. Find the measure of the angle.

Let x = the measure of "the angle". So the original angle, x, is 10 degrees. The supplement, 180-x, is 170 degrees. The compliment, 90-x, is 80 degrees.

Step-by-step explanation:

Now that we have expressions for all three angles we can translate the problem into an equation. Translating "The supplement of an angle is 10 more than twice its compliment" we get:

180-x [the supplement] = [is] 10+ [10 more than] 2*(90-x) [twice its complement]

180-x = 10 + 2(90-x)

Now we can use Algebra to solve. We start by simplifying:

180-x = 10 + 180 -2x

180-x = 190 -2x

Get the x's on just one side (by adding 2x to each side):

180+x = 190

Isolate the x (by subtracting 180 from each side):

x = 10

So the original angle, x, is 10 degrees.

The supplement, 180-x, is 170 degrees.

The compliment, 90-x, is 80 degrees.

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