Question

question 9b
lines eg and fh are parallel.
write an equation that represents the relationship between angle fcd and angle hcd.

Explanation:

Step1: Identify Angle Relationship

Since lines \( EG \) and \( FH \) are parallel, and \( CD \) is a transversal, angles \( \angle FCD \) and \( \angle HCD \) are adjacent and form a linear pair (they are supplementary, or their sum is \( 180^\circ \)), or if we consider vertical/alternate angles, but here they are adjacent on a straight line. Wait, actually, looking at the diagram, \( \angle FCD \) and \( \angle HCD \) are adjacent angles that form a linear pair, so their sum is \( 180^\circ \). Alternatively, if \( \angle FCD \) and \( \angle EBC \) are equal (corresponding angles), but the question is about \( \angle FCD \) and \( \angle HCD \). Wait, maybe \( \angle FCD + \angle HCD = 180^\circ \) because they are adjacent and form a straight line (linear pair).

Step2: Formulate the Equation

The linear pair postulate states that adjacent angles forming a straight line sum to \( 180^\circ \). So \( \angle FCD + \angle HCD = 180^\circ \).

Answer:

\( \angle FCD + \angle HCD = 180^\circ \)