Question

In the given figure, ACDF, ABEF, and BCDE are all parallelograms. Find the measurement of $\angle BCD$.

Answer 1

(i) $AF||BE$ (given)

(ii) $\angle AFE=\angle BED=z$

(iii) $\angle FBE=\angle FBE=x$ (alternate angles)

(iv) $\angle EBD=\angle CDB=y$ (alternate angles)

(v) $\therefore \angle FBD=x+y$ (from (iii) and (iv))

(vi) $\angle BCD=\angle BED=z$ (Opposite angles of a parallelogram)

(vi) $\angle CDG=\angle BED=z$ (Corresponding angles)