Question

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

Answer 1

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

\[
\angle ACB + \angle BCD = 180°
\]

Substituting the expressions for the angles:

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

Now, combine like terms:

\[
2x + 76 = 180
\]

Next, subtract 76 from both sides:

\[
2x = 180 - 76
\]

\[
2x = 104
\]

Now, divide by 2:

\[
x = 52
\]

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

\[
m∠BCD = x + 48 = 52 + 48 = 100°
\]

Thus, the measure of angle BCD is:

\[
\boxed{100°}
\]