Question

∠ACB
and ∠BCD
are supplementary angles. The angles have the following measures: ∡ACB=(x+28)°
and ∡BCD=(x+48)°
. What is m∠BCD
?(1 point)
Responses

80°
80 degrees

52°
52 degrees

128°
128 degrees

100°

Answer 1

To find the measure of angle \( m∠BCD \), we start with the fact that angles \( ∠ACB \) and \( ∠BCD \) are supplementary. This means their measures add up to \( 180° \).

Given:
- \( m∠ACB = (x + 28)° \)
- \( m∠BCD = (x + 48)° \)

We can write the equation:

\[
m∠ACB + m∠BCD = 180°
\]

Substituting the expressions for the angles, we get:

\[
(x + 28) + (x + 48) = 180
\]

Simplifying this:

\[
2x + 76 = 180
\]

Now, we solve for \( x \):

\[
2x = 180 - 76
\]
\[
2x = 104
\]
\[
x = 52
\]

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

\[
m∠BCD = x + 48 = 52 + 48 = 100°
\]

Thus, \( m∠BCD \) is \( 100° \).

So the answer is:

**100°**