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

Question

m∠ACB=___ °

Answer 1

Two angles are supplementary if the sum of their measures is 180 degrees. Given the two angles:

• \( m∠ACB = 4x \) degrees
• \( m∠BCD = (6x + 50) \) degrees

We can set up the equation as follows:

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

Now, combine like terms:

\[ 4x + 6x + 50 = 180 \] \[ 10x + 50 = 180 \]

Next, subtract 50 from both sides:

\[ 10x = 130 \]

Now, divide by 10:

\[ x = 13 \]

Now that we have the value of \( x \), we can find the measure of angle \( ∠ACB \):

\[ m∠ACB = 4x = 4(13) = 52 \]

Thus, the measure of \( ∠ACB \) is:

\[ \boxed{52} \text{°} \]