Two angles are supplementary with measures m∠ACB=4x° and m∠BCD=(6x+50)°. What is the measure of ∠ACB

Answer 1

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°.