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

100°
100 degrees

128°
128 degrees

52°

Answer 1

To find the measure of angle \( \angle BCD \), we can use the fact that \( \angle ACB \) and \( \angle BCD \) are supplementary angles. This means that their measures add up to \( 180^\circ \).

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

We can set up the equation:
\[
(x + 28) + (x + 48) = 180
\]

Combining like terms:
\[
2x + 76 = 180
\]

Now, subtract \( 76 \) from both sides:
\[
2x = 180 - 76
\]
\[
2x = 104
\]

Now divide both sides by \( 2 \):
\[
x = 52
\]

Now we can find \( m\angle BCD \):
\[
m\angle BCD = x + 48
\]
\[
m\angle BCD = 52 + 48 = 100
\]

So, the measure of \( \angle BCD \) is \( \boxed{100^\circ} \).