Question

The sum of two angle measures 130 degrees. The difference in the two angle measures is 12 degrees. What are the two angle measures ?

Answer 1

59°, 71°

Explanation:

This is a "sum and difference" problem. All problems of this type have the same answer: the larger of the two numbers is the average of those given.

Then the larger angle is (130 +12)°/2 = 71°. The smaller is 71° -12° = 59°.

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More detailed solution

There are several ways to get there using equations. You can, for example, let L represent the larger number. Then L - D will be the smaller one (where D represent the difference). The sum of the two numbers (S) is ...

L + (L -D) = S

2L = S + D . . . . collect terms, add D

L = (S+D)/2 . . . the larger number is the average of the sum and difference