Question

∠ACB and ∠BCD are supplementary angles. The angles have the following measures: ∡ACB=(x+28)° ∡ A C B = ( x + 28 ) ° and ∡BCD=(x+48)° ∡ B C D = ( x + 48 ) ° . What is m∠BCD m ∠ B C D ?(1 point) Responses 80° 80 degrees 52° 52 degrees 128° 128 degrees 100°

Answer 1

Given that angles ∠ACB and ∠BCD are supplementary, their measures add up to 180°. We can set up the equation based on their expressions:

\[
\angle ACB + \angle BCD = 180°
\]

Substituting the expressions for the angles:

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

Now, combine the terms:

\[
2x + 76 = 180
\]

Next, subtract 76 from both sides:

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

Now, divide both sides by 2:

\[
x = 52
\]

Now, we can find the measure of ∠BCD by substituting \(x\) back into the expression for ∠BCD:

\[
\angle BCD = x + 48 = 52 + 48 = 100°
\]

Thus, the measure of ∠BCD is:

\[
\boxed{100°}
\]