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

52°
52 degrees

100°
100 degrees

80°
80 degrees

128°

Answer 1

Since angles \( \angle ACB \) and \( \angle BCD \) are supplementary, their measures add up to 180 degrees.

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

We can set up the equation:
\[
m\angle ACB + m\angle BCD = 180^\circ
\]
Substituting the expressions for the angles:
\[
(x + 28) + (x + 48) = 180
\]

Now, simplify and solve for \( x \):
\[
2x + 76 = 180
\]
\[
2x = 180 - 76
\]
\[
2x = 104
\]
\[
x = 52
\]

Now that we know \( x \), we can find \( m\angle BCD \):
\[
m\angle BCD = x + 48 = 52 + 48 = 100^\circ
\]

Thus, the measure of \( \angle BCD \) is:
\[
\boxed{100^\circ}
\]