∠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°

1 answer

To solve for \( m\angle BCD \), we first set up the equation based on the information given about supplementary angles. Supplementary angles sum to \( 180^\circ \).

Given:

  • \( m\angle ACB = (x + 28)^\circ \)
  • \( m\angle BCD = (x + 48)^\circ \)

Since they are supplementary, we can write the equation:

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

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 \( m\angle BCD \):

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

Therefore,

\[ m\angle BCD = 100^\circ \]

The answer is \( \boxed{100^\circ} \).