Question

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

°

Answer 1

To find the measure of angle \( m∠ACB \), we know that supplementary angles add up to \( 180^\circ \). In this case, we have:

\[
m∠ACB + m∠BCD = 180^\circ
\]

Substituting the expressions for 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 we can find \( m∠ACB \):

\[
m∠ACB = 4x = 4(13) = 52^\circ
\]

Thus, the measure of \( ∠ACB \) is

\[
\boxed{52^\circ}
\]