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 their measures add up to 180°. Thus, we can set up the equation:

\[ m∠ACB + m∠BCD = 180° \]

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 both sides by 10:

\[ x = 13 \]

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

\[ m∠ACB = 4x = 4(13) = 52° \]

Thus, the measure of angle \( ∠ACB \) is:

\[ \boxed{52} \]