24. AD || BC, ∠1 : ∠2 = 5 : 11 , ∠1, ∠2 — ?

Since AD || BC, the interior angles on the same side of the transversal sum to 180 degrees. Therefore, $$\angle 1 + \angle 2 + 80^{\circ} = 180^{\circ}$$, so $$\angle 1 + \angle 2 = 100^{\circ}$$. Given the ratio $$\angle 1 : \angle 2 = 5 : 11$$, let $$\angle 1 = 5x$$ and $$\angle 2 = 11x$$. Then $$5x + 11x = 100^{\circ}$$, so $$16x = 100^{\circ}$$, therefore $$x = \frac{100}{16} = \frac{25}{4} = 6.25^{\circ}$$. Thus, $$\angle 1 = 5 \cdot 6.25 = 31.25^{\circ}$$ and $$\angle 2 = 11 \cdot 6.25 = 68.75^{\circ}$$. **Answer: ∠1 = 31.25°, ∠2 = 68.75°**