Two angles are supplementary with measures m ACB = 4x degrees and m BCD = (6x + 60) degrees. What is the measure of ACB?

m ACB = __ degrees

1 answer

To find the measure of angle ACB, we need to set up an equation using the fact that supplementary angles add up to 180 degrees.

Given:
m ACB = 4x degrees
m BCD = (6x + 60) degrees

Since ACB and BCD are supplementary angles:
m ACB + m BCD = 180

Substitute the given measures:
4x + (6x + 60) = 180

Combine like terms:
10x + 60 = 180

Subtract 60 from both sides:
10x = 120

Divide by 10:
x = 12

Now plug x back into the measure of angle ACB:
m ACB = 4x
m ACB = 4(12)
m ACB = 48 degrees

Therefore, the measure of angle ACB is 48 degrees.