Two angles are supplementary with measures m∠ACB=4x°

Question

and m∠BCD=(6x+50)°
. What is the measure of ∠ACB
?(1 point)
m∠ACB=__

Answer 1

Two angles are supplementary when the sum of their measures is 180 degrees. Therefore, we can set up the following equation:

\[ m∠ACB + m∠BCD = 180° \]

Substituting the measures of the angles:

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

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:

\[ m∠ACB = 52° \]