∠ACB

Question

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

128°
128 degrees

52°
52 degrees

80°
80 degrees

100°

Answer 1

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

\[ m∠ACB + m∠BCD = 180° \]

Substituting the expressions for the angles:

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

Combining like terms:

\[ 2x + 76 = 180 \]

Next, we solve for \(x\):

\[ 2x = 180 - 76 \] \[ 2x = 104 \] \[ x = 52 \]

Now we can find \(m∠BCD\):

\[ m∠BCD = x + 48 = 52 + 48 = 100° \]

So, the measure of angle \(BCD\) is 100°.