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 if the sum of their measures equals \(180^\circ\). Given that:

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

We can set up the equation:

\[ m∠ACB + m∠BCD = 180^\circ \]

Substituting the expressions for the angles into the equation:

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

Simplifying the left side:

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

Now, subtract \(50\) from both sides:

\[ 10x = 130 \]

Next, divide by \(10\):

\[ x = 13 \]

Now, we can find \(m∠ACB\):

\[ m∠ACB = 4x = 4(13) = 52^\circ \]

Thus, the measure of \(∠ACB\) is:

\[ m∠ACB = 52^\circ \]