Two angles are supplementary with measures m<ACB =4x and m<BCD=(6x+50) What is the measure of <ACB?
Since two angles are supplementary, their measures add up to 180 degrees. Therefore, we have the equation:
m<ACB + m<BCD = 180
Substituting in the given measures:
4x + (6x + 50) = 180
Combining like terms:
10x + 50 = 180
Subtracting 50 from both sides:
10x = 130
Dividing both sides by 10:
x = 13
Therefore, the measure of <ACB is:
m<ACB = 4x = 4(13) = 52 degrees. Answer: \boxed{52}.