To find the measure of angle \( \angle BCD \), we first note that since the angles \( \angle ACB \) and \( \angle BCD \) are supplementary, their measures add up to \( 180^\circ \).
Given the measures: \[ m\angle ACB = (x + 28)^\circ \] \[ m\angle BCD = (x + 48)^\circ \]
We can set up the equation: \[ (x + 28) + (x + 48) = 180 \]
Now, let's combine like terms: \[ 2x + 76 = 180 \]
Next, we'll solve for \( x \) by subtracting \( 76 \) from both sides: \[ 2x = 180 - 76 \] \[ 2x = 104 \]
Now, divide by \( 2 \): \[ x = 52 \]
Now that we have \( x \), we can find the measure of \( \angle BCD \): \[ m\angle BCD = (x + 48) = 52 + 48 = 100^\circ \]
Thus, \( m\angle BCD \) is \( \boxed{100^\circ} \).
16 answers