What type of map projection shows the correct sizes of countries but distorts angles?

The correct choice is the equal-area projection. This type of map projection is specifically designed to ensure that the sizes of areas are represented accurately relative to each other. In an equal-area projection, the shapes of countries are distorted, meaning that angles and the overall geometry can be altered to maintain proportional area. This is particularly useful in applications where accurate representation of landmass sizes is critical, such as in demographic studies and resource allocation.

An important characteristic of equal-area projections is that they maintain the correct ratio of area, making them valuable for geographical analysis that prioritizes land distribution over angular accuracy. This contrasts with conformal projections, which preserve angles but often distort the size of areas, and other types of projections that focus on different aspects such as distance or typical representations of the earth.