Question

If the supplement of an acute angle has a measure of (2x+44), find, in terms of x, the measure of the complement of the acute angle...

Answer 1

complement of acute angle = 2x - 46

Explanation:

supplementary angles sum to 180° , that is

acute angle + supplement = 180

acute angle + (2x + 44) = 180 ( subtract 2x + 44 from both sides )

acute angle = 180 - (2x + 44) = 180 - 2x - 44 = 136 - 2x

complementary angles sum to 90° , that is

acute angle + complement = 90

136 - 2x + complement = 90 ( subtract 136 - 2x from both sides )

complement = 90 - (136 - 2x) = 90 - 136 + 2x = 2x - 46