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Let x = the measure of "the angle".
Then the supplement is: 180-x
and the compliment is: 90-x
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.