1997 AMC 8 第 12 题

Use the supplementary condition and then angle $3$ equals angle $4$

First find angle $1$ from the left triangle

We have that $$\angle 1 = 180^{\circ} - 70^{\circ} - 40^{\circ} = 70^{\circ}$$ using the fact that the interior angles of a triangle add to $180^{\circ}.$

This tells us that $$\angle 2 = 180^{\circ} - \angle 1 = 110^{\circ}$$ since $\angle 1$ and $\angle 2$ are supplementary.

Finally, $$\angle 3 + \angle 4 + 110^{\circ} = 180^{\circ} \Rightarrow$$$$2 \angle 4 = 70^{\circ} \Rightarrow \angle 4 = 35^{\circ}.$$

Thus, D is the correct answer.