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.

$x = 52 \div 2 = 26$
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°