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

Answer 1

Complementary angles are two angles whose sum is 90 degrees.

Let's denote the measure of the first angle as A and the measure of the second angle as B.

We are given that these angles are expressed in separate terms of (2x-6) and (2x).

So, we can write the equation A + B = 90.

Substituting the given expressions, we have:
(2x-6) + (2x) = 90

Combining like terms:
4x - 6 = 90

Adding 6 to both sides:
4x = 96

Dividing both sides by 4:
x = 24

Now, let's find the measures of the two angles:

For angle A:
A = 2x - 6
A = 2(24) - 6
A = 48 - 6
A = 42 degrees

For angle B:
B = 2x
B = 2(24)
B = 48 degrees

Therefore, angle A measures 42 degrees and angle B measures 48 degrees.