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.
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.