Two angles are supplementary with measures m∠ACB=4x° and m∠BCD=(6x+50)° . What is the measure of ∠ACB ?
The sum of supplementary angles is always 180 degrees.
So, we have the equation:
m∠ACB + m∠BCD = 180
Substituting the given values, we get:
4x + (6x + 50) = 180
Combining like terms,
10x + 50 = 180
Subtracting 50 from both sides,
10x = 130
Dividing both sides by 10,
x = 13
Finally, we can find the measure of ∠ACB by substituting the value of x into the equation for m∠ACB:
m∠ACB = 4x
m∠ACB = 4 * 13
m∠ACB = 52 degrees. Answer: \boxed{52}.