Two angles are supplementary with measures m∠ACB=4x° and m∠BCD=(6x+50)°. What is the measure of ∠ACB?
Since the two angles are supplementary, their sum is 180 degrees. Therefore, we have the equation:
m∠ACB + m∠BCD = 180
Plugging in the given values, we have:
4x + (6x + 50) = 180
Combining like terms, we have:
10x + 50 = 180
Subtracting 50 from both sides, we have:
10x = 130
Dividing both sides by 10, we have:
x = 13
Finally, plugging this value back into the equation m∠ACB = 4x, we get:
m∠ACB = 4(13) = 52 degrees
Therefore, the measure of ∠ACB is 52 degrees.