Two complementary angles are expressed in terms of (2x-6) and (2x). Write and solve an equation for x, and give the measure of the 2 angles.

Answer 1

Let the measure of the first angle be (2x - 6) degrees.
The measure of its complement will be 90 - (2x - 6) = 90 - 2x + 6 = 96 - 2x degrees.
According to the definition of complementary angles, these two measures must add up to 90 degrees.
(2x - 6) + (96 - 2x) = 90
Combining like terms gives 96 - 6 = 90
Simplifying further gives 90 = 90.
The equation is true for all values of x.