∠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

128°
  128 degrees

80°

1 answer

Since angles ∠ACB and ∠BCD are supplementary, their measures add up to 180°:

\[ m∠ACB + m∠BCD = 180° \]

Given the measures of the angles:

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

Now, combine like terms:

\[ 2x + 76 = 180 \]

Next, solve for \(x\) by subtracting 76 from both sides:

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

Now, divide by 2:

\[ x = 52 \]

Now we can find the measure of ∠BCD:

\[ m∠BCD = x + 48 \] \[ m∠BCD = 52 + 48 = 100° \]

Therefore, the measure of ∠BCD is 100°.