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

128°
128 degrees

52°
52 degrees

80°
80 degrees

100°

Answer 1

To determine the measure of angle \( \angle BCD \), we can use the fact that supplementary angles add up to \( 180^\circ \).

Given:
- \( m\angle ACB = (x + 28)^\circ \)
- \( m\angle BCD = (x + 48)^\circ \)

Because these angles are supplementary, we set up the following equation:

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

Now, let's combine like terms:

\[
2x + 76 = 180
\]

Next, we will isolate \( 2x \) by subtracting \( 76 \) from both sides:

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

Now, divide both sides by \( 2 \):

\[
x = 52
\]

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

\[
m\angle BCD = x + 48 = 52 + 48 = 100^\circ
\]

Thus, the measure of \( \angle BCD \) is:

\[
\boxed{100^\circ}
\]