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In the diagram, ℓ$_{5}$ ∥ ℓ$_{4}$, and ℓ$_{3}$ ∥ ℓ$_{2}$. The transversals ℓ$_{6}$ and ℓ$_{1}$ cut the parallel lines. The marked angles are 62°, 35°, 128°, 31° and 66°. Calculate the value of each marked unknown, giving a reason for every answer.

Study the diagram: ℓ$_{5}$ ∥ ℓ$_{1}$, and ℓ$_{4}$ ∥ ℓ$_{2}$. The transversals ℓ$_{6}$ and ℓ$_{3}$ cut the parallel lines. The marked angles are 153°, 78°, 75°, 38° and 153°. Calculate the value of each marked unknown, giving a reason for every answer.

In the figure, ℓ$_{4}$ ∥ ℓ$_{5}$, and ℓ$_{3}$ ∥ ℓ$_{6}$. The transversals ℓ$_{2}$ and ℓ$_{1}$ cut the parallel lines. The marked angles are 97°, 34°, 97°, 63° and 45°. Calculate the value of each marked unknown, giving a reason for every answer.

An isosceles triangle has an altitude of 13 cm drawn from its apex perpendicular to its base. The base measures 20 cm. Calculate the value of each marked unknown, giving a reason for every answer.

In the diagram, ℓ$_{6}$ ∥ ℓ$_{1}$, and ℓ$_{3}$ ∥ ℓ$_{2}$. The transversals ℓ$_{5}$ and ℓ$_{4}$ cut the parallel lines. The marked angles are 108°, 72°, 108°, 108° and 50°. Calculate the value of each marked unknown, giving a reason for every answer.

In the figure, ℓ$_{1}$ ∥ ℓ$_{2}$, and ℓ$_{4}$ ∥ ℓ$_{3}$. The transversals ℓ$_{5}$ and ℓ$_{6}$ cut the parallel lines. The marked angles are 29°, 47°, 29°, 138° and 91°. Calculate the value of each marked unknown, giving a reason for every answer.

Study the diagram: ℓ$_{1}$ ∥ ℓ$_{2}$, and ℓ$_{4}$ ∥ ℓ$_{3}$. The transversals ℓ$_{5}$ and ℓ$_{6}$ cut the parallel lines. The marked angles are 43°, 73°, 30°, 114° and 41°. Calculate the value of each marked unknown, giving a reason for every answer.

Study the diagram: ℓ$_{3}$ ∥ ℓ$_{4}$, and ℓ$_{5}$ ∥ ℓ$_{2}$. The transversals ℓ$_{1}$ and ℓ$_{6}$ cut the parallel lines. The marked angles are 34°, 53°, 39°, 141° and 88°. Calculate the value of each marked unknown, giving a reason for every answer.

Study the diagram: ℓ$_{4}$ ∥ ℓ$_{6}$, and ℓ$_{5}$ ∥ ℓ$_{2}$. The transversals ℓ$_{1}$ and ℓ$_{3}$ cut the parallel lines. The marked angles are 76°, 29°, 104°, 75° and 46°. Calculate the value of each marked unknown, giving a reason for every answer.

Study the diagram: ℓ$_{1}$ ∥ ℓ$_{3}$, and ℓ$_{4}$ ∥ ℓ$_{2}$. The transversals ℓ$_{5}$ and ℓ$_{6}$ cut the parallel lines. The marked angles are 150°, 34°, 150°, 42° and 108°. Calculate the value of each marked unknown, giving a reason for every answer.

Study the diagram: ℓ$_{5}$ ∥ ℓ$_{1}$, and ℓ$_{3}$ ∥ ℓ$_{2}$. The transversals ℓ$_{4}$ and ℓ$_{6}$ cut the parallel lines. The marked angles are 100°, 42°, 67°, 100° and 33°. Calculate the value of each marked unknown, giving a reason for every answer.

In the figure, ℓ$_{6}$ ∥ ℓ$_{2}$, and ℓ$_{3}$ ∥ ℓ$_{5}$. The transversals ℓ$_{4}$ and ℓ$_{1}$ cut the parallel lines. The marked angles are 139°, 47°, 59°, 33° and 92°. Calculate the value of each marked unknown, giving a reason for every answer.