Two angles are supplementary with measures  m∠ACB=4x° and m∠BCD=(6x+50)° . What is the measure of ∠ACB ?(1 point)

m∠ACB= ___°

1 answer

Two angles are supplementary, which means their sum is 180 degrees. Given the measures of the angles:

\[ m∠ACB = 4x° \] \[ m∠BCD = (6x + 50)° \]

We can set up the equation:

\[ 4x + (6x + 50) = 180 \]

Combine like terms:

\[ 10x + 50 = 180 \]

Now, subtract 50 from both sides:

\[ 10x = 130 \]

Next, divide both sides by 10:

\[ x = 13 \]

Now, we can find the measure of angle \( m∠ACB \):

\[ m∠ACB = 4x = 4(13) = 52° \]

Therefore, the measure of \( ∠ACB \) is:

\[ \boxed{52°} \]