SOLUTION: when you add the measure of an angle to twice the measure of its complement, the sum is the measure of the angles supplement.

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Question 1157256: when you add the measure of an angle to twice the measure of its complement, the sum is the measure of the angles supplement.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Two Angles are Supplementary when they add up to 180 degrees.
Two Angles are Complementary when they add up to 90 degrees.
let an angle be alpha
its complement is 90-alpha
and its supplement is 180-alpha
when you add the measure of an angle to twice the measure of its complement, we have
alpha%2B2%2890-alpha%29
the sum is the measure of the angles supplement, 180-alpha

set up equation and prove it is true statement:

alpha%2B2%2890-alpha%29=180-alpha......solve for alpha
alpha%2B180-2alpha=180-alpha
2alpha%2B180-2alpha-180=0
0=0=> true

an examples to show that, when you add the measure of an angle to twice the measure of its complement, the sum is the measure of the angle's supplement:

let's say that the angle alpha=30 degrees
so, we have
alpha%2B2%2890-alpha%29=180-alpha
30%2B2%2890-30%29=180-30
30+%2B+120+=+150
150+=+150

same will be if alpha=60 degrees, alpha=45 degrees, alpha=1 degrees,....