Question

Two angles are complementary. their difference is 38. find the angles

Answer 1

Hi there! The answer is 26° and 64°.

The sum of the complementary angles is (always) 90°. Let the smallest angle be represented by x. Then we get the following sum of angles.


`x + (x + 38) = x + x + 38 = 2x + 38`
This sum equals 90°, so we get


`2x + 38 = 90`
Subtract 38 from both sides.


`2x = 52`
Divide both sides by 2.


`x = 52 / 2 = 26`
Now we now that the smallest angle measures 26°. The bigger angle measures x + 38, so


`x + 38 = 26 + 38 = 64`
Hence, the angles measure 26° and 64°