Concept 1

Use angle relationships (parallel lines, polygons) and triangle properties.

Most angle problems reduce to a few standard facts about lines, triangles, and polygons.

Core Idea

Most ACT angle questions reduce to a short rule: vertical angles are equal, a linear pair sums to $180 \circ$ , triangle interior angles sum to $180 \circ$ , and polygon or parallel-line relationships finish the rest.

Understanding

Rule: The key is choosing the right angle fact quickly. If lines intersect, check for vertical angles or a linear pair. If lines are parallel, look for corresponding, alternate interior, or same-side interior relationships. If the figure is a triangle or polygon, use angle sums and any special properties such as isosceles base angles.

Once the correct rule is identified, the rest is usually a one-step equation or direct subtraction.

Question

Worked Example

In triangle $𝑃 𝑄 𝑅$ , two interior angles measure $48 \circ$ and $67 \circ$ . What is the measure of the exterior angle at the third vertex?

Select an answer to see the explanation