Lesson 1: Angle Relationships

Property

An angle consists of two rays which share the same vertex.
A straight angle is half a full rotation and has a measure of $180^\circ$. 123
A right angle has a measure of $90^\circ$.
An acute angle measures less than $90^\circ$.
An obtuse angle measures greater than $90^\circ$ and less than $180^\circ$.

Examples

• The corner of a standard sheet of paper forms a perfect right angle, measuring exactly $90^\circ$.
• A slice from a round cake usually has a sharp point at the center, which is an acute angle (less than $90^\circ$).
• When you recline in a chair, the angle between the seat and the back becomes obtuse, measuring more than $90^\circ$.

Explanation

We classify angles by comparing them to a square corner ($90^\circ$) and a straight line ($180^\circ$). This special vocabulary helps us describe the corners and turns in any shape, telling us if they are sharp, square, or wide.

Property

If the sum of the measures of two angles is 180°, then the angles are supplementary.

If the sum of the measures of two angles is 90°, then the angles are complementary.

Examples

• An angle measures 70°. Its supplement is 180° - 70° = 110° because supplementary angles must add up to 180°.
• An angle measures 35°. Its complement is 90° - 35° = 55° because complementary angles must add up to 90°.