Question

TWo angles are supplementary with measures m angle ACB =4x and m angle BCD = (6x + 50) what is the measure of angle ACB

Answer 1

Two angles are supplementary if their measures add up to \(180^\circ\). Given:

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

Since these angles are supplementary, we can set up the equation:

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

Now, combine like terms:

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

This simplifies to:

\[
10x + 50 = 180
\]

Next, subtract 50 from both sides:

\[
10x = 130
\]

Now, divide by 10:

\[
x = 13
\]

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

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

Thus, the measure of angle \(ACB\) is \(52^\circ\).