Find the measure of (a) the complement and (b) the supplement of ...

Question

Find the measure of (a) the complement and (b) the supplement of an angle with the given measure. See Examples 1 and 3.                                                                                                                                                             
                                                                                                                                                                                                                                                                                                                                                                                 
  10°

Accepted Answer

Hello, everyone. We are asked for the following angle to solve for the degree measure of its complement and supplement, we are given eight degrees. Our answer choices are a complement degrees. Supplement 127 degrees. B complement 127 degrees. Supplement 37 degrees. C complement 172 degrees. Supplement 82 degrees. D complement 82 degrees. Supplement 172 degrees. First, we need to recall that complementary angles total, we have a sum of 90 degrees. So this is like saying eight degrees plus some unknown angle X totals to 90 degrees. So to find the unknown angle, I will subtract eight degrees from each side and we get that X equals 82 degrees. So this is our compliment. Continuing on to find the supplement. We remember that uh supplementary angles have a son of 180 degrees. So we'll set this up similarly eight degrees plus some unknown angle X has to total to 180 degrees. Subtracting eight degrees from both sides. I get that my unknown angle X would have to equal 172 degrees. And this is our supplement. So now knowing the complement is 82 degrees and the supplement is 172 degrees. I look at my answer choices and that is answer choice. D have a nice day.

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Find the measure of (a) the complement and (b) the supplement of an angle with the given measure. See Examples 1 and 3. 10°