Geometry Lesson · Grades 6–9

Adjacent and Vertical Angles

A geometry lesson on the relationships between pairs of angles. Students learn to identify adjacent angles, vertical angles, and linear pairs from diagrams — then practice with a 20-question worksheet.

Reading Passage

Adjacent and Vertical Angles

When we have a pair of angles together, there can be a relationship that defines the pair. Two of the most common are adjacent angles and vertical angles.

Adjacent angles are two angles that are next to each other and share a common vertex and a common ray. The key word is next. If a line segment AB is bisected by a line segment DO, the resulting two angles — ∠AOD and ∠DOB — share the ray OD and the vertex O. They are adjacent angles.

Vertical angles are formed when two lines intersect. They are opposite each other and are not adjacent. When two lines cross, they form two pairs of vertical angles. Vertical angles are always equal in measure (congruent).

Two adjacent angles whose non-shared rays form a straight line are called a linear pair. A linear pair always adds up to 180° — the measure of a straight angle.

Knowing these relationships lets you find unknown angle measures in a diagram without using a protractor. If two angles are vertical, they are equal. If two angles form a linear pair, they add to 180°. With practice, you can read a diagram and find every angle measure from just one or two given values.

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