Angle chase (parallel lines)

In the diagram, ℓ$_{3}$ ∥ ℓ$_{6}$, and ℓ$_{5}$ ∥ ℓ$_{1}$. The transversals ℓ$_{4}$ and ℓ$_{2}$ cut the parallel lines. The marked angles are 97°, 38° and 55°. Calculate, with reasons, the size of w.

In the figure, ℓ$_{1}$ ∥ ℓ$_{4}$ ∥ ℓ$_{5}$. The transversals ℓ$_{3}$ and ℓ$_{2}$ cut the parallel lines. The marked angles are 44° and 104°. Calculate, with reasons, the size of y.

Study the diagram: ℓ$_{1}$ ∥ ℓ$_{4}$ ∥ ℓ$_{5}$. The transversals ℓ$_{3}$ and ℓ$_{2}$ cut the parallel lines. The marked angles are 51° and 104°. Calculate, with reasons, the size of y.

Study the diagram: ℓ$_{4}$ ∥ ℓ$_{1}$. The transversals ℓ$_{2}$ and ℓ$_{3}$ cut the parallel lines. The marked angles are 81° and 120°. Calculate, with reasons, the size of y.

In the figure, ℓ$_{2}$ ∥ ℓ$_{3}$. The transversals ℓ$_{4}$ and ℓ$_{1}$ cut the parallel lines. The marked angle is 60°. Calculate, with reasons, the size of r.

In the figure, ℓ$_{3}$ ∥ ℓ$_{4}$, and ℓ$_{1}$ ∥ ℓ$_{2}$. The transversals ℓ$_{6}$ and ℓ$_{5}$ cut the parallel lines. The marked angles are 99° and 66°. Calculate, with reasons, the size of d.

In the figure, ℓ$_{4}$ ∥ ℓ$_{1}$ ∥ ℓ$_{3}$. The transversals ℓ$_{5}$ and ℓ$_{2}$ cut the parallel lines. The marked angle is 98°. One angle is marked $5x-13^\circ$. Calculate the value of x, giving reasons.

In the figure, ℓ$_{5}$ ∥ ℓ$_{1}$ ∥ ℓ$_{3}$. The transversals ℓ$_{4}$ and ℓ$_{2}$ cut the parallel lines. The marked angle is 122°. One angle is marked $2x+20^\circ$. Calculate the value of x, giving reasons.

Study the diagram: ℓ$_{2}$ ∥ ℓ$_{3}$. The transversals ℓ$_{1}$ and ℓ$_{4}$ cut the parallel lines. The marked angles are 48° and 95°. Calculate, with reasons, the size of p.

In the diagram, ℓ$_{3}$ ∥ ℓ$_{2}$ ∥ ℓ$_{1}$. The transversals ℓ$_{5}$ and ℓ$_{4}$ cut the parallel lines. The marked angles are 42° and 76°. One angle is marked $5x+28^\circ$. Calculate the value of x, giving reasons.

Study the diagram: ℓ$_{2}$ ∥ ℓ$_{1}$. The transversals ℓ$_{4}$ and ℓ$_{3}$ cut the parallel lines. The marked angles are 72° and 96°. Calculate, with reasons, the size of h.

Study the diagram: ℓ$_{2}$ ∥ ℓ$_{6}$, and ℓ$_{3}$ ∥ ℓ$_{1}$. The transversals ℓ$_{5}$ and ℓ$_{4}$ cut the parallel lines. The marked angles are 52°, 44° and 35°. Calculate, with reasons, the size of z.