∠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 100° 100 degrees 128° 128 degrees 52° 52 degrees 80°

Answer 1

Since ∠ACB and ∠BCD are supplementary angles, their measures add up to 180°. Therefore, we can set up the following equation:

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

Combining like terms gives:

\[ 2x + 76 = 180 \]

Subtracting 76 from both sides:

\[ 2x = 104 \]

Dividing by 2:

\[ x = 52 \]

Now, we can find the measure of ∠BCD:

\[ m∠BCD = x + 48 = 52 + 48 = 100° \]

Thus, the measure of ∠BCD is \( \boxed{100°} \).