Question

1. a e c 8x° b 4x° d x = m∠bcd =

Explanation:

Step1: Identify supplementary angles

Angles \( \angle ACB = 8x^\circ \) and \( \angle BCD = 4x^\circ \) are supplementary (form a linear pair), so their sum is \( 180^\circ \).
\[ 8x + 4x = 180 \]

Step2: Solve for \( x \)

Combine like terms:
\[ 12x = 180 \]
Divide both sides by 12:
\[ x = \frac{180}{12} = 15 \]

Step3: Find \( m\angle BCD \)

Substitute \( x = 15 \) into \( 4x^\circ \):
\[ m\angle BCD = 4(15) = 60^\circ \]

Answer:

\( x = 15 \), \( m\angle BCD = 60^\circ \)