Lessons 40: Sum of the Angle Measures of a Triangle, Angle Pairs

New Concept

The three angles of every triangle have measures that total $180^\circ$. Two angles are supplementary if their sum is $180^\circ$, complementary if their sum is $90^\circ$, and vertical if they are opposite angles formed by intersecting lines, in which case they are equal.

What’s next

This is just the beginning. Next, you'll tackle worked examples and challenge problems to find unknown angles in various geometric figures.

Property

The three angles of every triangle have measures that total 180°.

Examples

• In a triangle with angles 50° and 70°, the third angle is 180° - 120° = 60°.
• A right triangle with a 25° angle has a third angle of 180° - 90° - 25° = 65°.
• An equilateral triangle has three equal angles, so each angle must be 180° ÷ 3 = 60°.

Explanation

Imagine tearing the three corners off any paper triangle and lining them up. No matter the triangle's shape, the three angles will always fit together perfectly to form a straight line, which is exactly 180°! It's a math magic trick that always works.

Property

Two angles whose sum is $180^\circ$ are called supplementary angles.

Examples

If $\angle A = 110^\circ$, its supplement, $\angle B$, is $180^\circ - 110^\circ = 70^\circ$.
Two adjacent angles on a straight line, such as $45^\circ$ and $135^\circ$, are always supplementary.

Explanation

Think of supplementary angles as buddies who complete a straight line. If you know one angle, you can always find its partner's size. Together they form a perfect $180^\circ$ straight angle, making them perfectly balanced partners in geometry! They are a 'supplement' to each other.