Question

Two angles are supplementary with measures m<ACD = 4x and m<BCD = ( 6x + 50 ) wut is da measure of <ACB?

m<ACB = ____

Answer 1

To find the measure of angle \( ACB \), we start with the information given about the angles.

Angles \( ACD \) and \( BCD \) are supplementary, which means their measures add up to \( 180^\circ \). We have:

\[
m \angle ACD = 4x
\]
\[
m \angle BCD = 6x + 50
\]

Since the angles are supplementary, we can write the equation:

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

Now, combine like terms:

\[
10x + 50 = 180
\]

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 measures of angles \( ACD \) and \( BCD \).

First, calculate \( m \angle ACD \):

\[
m \angle ACD = 4x = 4(13) = 52^\circ
\]

Next, calculate \( m \angle BCD \):

\[
m \angle BCD = 6x + 50 = 6(13) + 50 = 78 + 50 = 128^\circ
\]

Now we need to find the measure of angle \( ACB \). Since \( ACB \) and \( ACD \) are part of the same straight line (assuming \( A \), \( C \), and \( B \) are on the same line), \( m \angle ACB \) can be calculated by finding the supplement of \( m \angle ACD \):

\[
m \angle ACB = 180^\circ - m \angle ACD
\]

Substituting \( m \angle ACD \):

\[
m \angle ACB = 180^\circ - 52^\circ = 128^\circ
\]

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

\[
\boxed{128^\circ}
\]