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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

Two angles are supplementary if the sum of their measures equals 180°. Given the measures of angle ACB and angle BCD as follows:

- \( m∠ACB = 4x° \)
- \( m∠BCD = (6x + 50)° \)

Set up the equation based on the definition of supplementary angles:

\[
m∠ACB + m∠BCD = 180°
\]

Substituting the expressions for the angles:

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

Simplify the equation:

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

Combine like terms:

\[
10x + 50 = 180
\]

Now, subtract 50 from both sides:

\[
10x = 130
\]

Next, divide by 10:

\[
x = 13
\]

Now, substitute \( x \) back into the expression for \( m∠ACB \):

\[
m∠ACB = 4x = 4(13) = 52°
\]

Thus, the measure of \( ∠ACB \) is:

\[
\boxed{52}
\]