Two angles are supplementary with measures m∠ACB=4x° and m∠BCD=(6x+50)°. What is the measure of ∠ACB?
m∠ACB= ___
Since two angles are supplementary, their measures add up to 180°. So, we have the equation 4x + 6x + 50 = 180.
Combining like terms, we get 10x + 50 = 180.
Subtracting 50 from both sides, we have 10x = 130.
Dividing both sides by 10, we obtain x = 13.
To find the measure of ∠ACB, we substitute x = 13 into the expression 4x.
m∠ACB = 4(13) = 52°.
Therefore, the measure of ∠ACB is 52°.