Two angles are supplementary with measures m∠ACB=4x° and m∠BCD=(6x+50)°. What is the measure of ∠ACB
Given that the two angles are supplementary, their measures add up to 180 degrees.
So, the equation is :
m∠ACB + m∠BCD = 180°
Substitute the given angle measures into the equation:
4x + (6x + 50) = 180
Combine like terms:
10x + 50 = 180
Subtract 50 from both sides:
10x = 130
Divide by 10:
x = 13
Now substitute back into the equation to find the measure of angle ACB:
m∠ACB = 4x
m∠ACB = 4(13)
m∠ACB = 52°
Therefore, the measure of angle ACB is 52°.