Angle chase (parallel lines)

In the diagram, ℓ$_{2}$ ∥ ℓ$_{4}$ ∥ ℓ$_{3}$. The transversals ℓ$_{1}$ and ℓ$_{5}$ cut the parallel lines. The marked angles are 124° and 42°. One angle is marked $4x+34^\circ$. Calculate the value of x, giving reasons.

In the figure, ℓ$_{4}$ ∥ ℓ$_{2}$ ∥ ℓ$_{1}$. The transversals ℓ$_{3}$ and ℓ$_{5}$ cut the parallel lines. The marked angle is 76°. One angle is marked $3x+35^\circ$. Calculate the value of x, giving reasons.

In the figure, ℓ$_{2}$ ∥ ℓ$_{3}$. The transversals ℓ$_{4}$ and ℓ$_{1}$ cut the parallel lines. The marked angles are 119° and 52°. Calculate, with reasons, the size of r.

Study the diagram: ℓ$_{1}$ ∥ ℓ$_{3}$ ∥ ℓ$_{5}$. The transversals ℓ$_{4}$ and ℓ$_{2}$ cut the parallel lines. The marked angles are 68° and 62°. Calculate, with reasons, the size of n.

In the diagram, ℓ$_{2}$ ∥ ℓ$_{5}$ ∥ ℓ$_{1}$. The transversals ℓ$_{3}$ and ℓ$_{4}$ cut the parallel lines. The marked angle is 39°. Calculate, with reasons, the size of c.

Study the diagram: ℓ$_{6}$ ∥ ℓ$_{5}$, and ℓ$_{4}$ ∥ ℓ$_{1}$. The transversals ℓ$_{3}$ and ℓ$_{2}$ cut the parallel lines. The marked angles are 55° and 49°. Calculate, with reasons, the size of s.

Study the diagram: ℓ$_{1}$ ∥ ℓ$_{2}$. The transversals ℓ$_{4}$ and ℓ$_{3}$ cut the parallel lines. The marked angles are 46° and 92°. Calculate, with reasons, the size of s.

Study the diagram: ℓ$_{4}$ ∥ ℓ$_{3}$. The transversals ℓ$_{1}$ and ℓ$_{2}$ cut the parallel lines. The marked angles are 47° and 68°. Calculate, with reasons, the size of h.

In the figure, ℓ$_{1}$ ∥ ℓ$_{3}$, and ℓ$_{2}$ ∥ ℓ$_{5}$. The transversals ℓ$_{4}$ and ℓ$_{6}$ cut the parallel lines. The marked angles are 71° and 100°. Calculate, with reasons, the size of b.

Study the diagram: ℓ$_{2}$ ∥ ℓ$_{5}$, and ℓ$_{1}$ ∥ ℓ$_{6}$. The transversals ℓ$_{4}$ and ℓ$_{3}$ cut the parallel lines. The marked angles are 45° and 47°. Calculate, with reasons, the size of g.

In the figure, ℓ$_{2}$ ∥ ℓ$_{1}$ ∥ ℓ$_{5}$. The transversals ℓ$_{3}$ and ℓ$_{4}$ cut the parallel lines. The marked angle is 91°. One angle is marked $5x+29^\circ$. Calculate the value of x, giving reasons.

Study the diagram: ℓ$_{1}$ ∥ ℓ$_{5}$ ∥ ℓ$_{3}$. The transversals ℓ$_{2}$ and ℓ$_{4}$ cut the parallel lines. The marked angle is 93°. One angle is marked $3x+24^\circ$. Calculate the value of x, giving reasons.