Lesson 1: Measuring Angles

Property

A line segment is determined by two points, called its endpoints.
A ray is a piece of a line that extends from one point (called the vertex) on and on in only one direction.
An angle is formed by two rays that share a common endpoint called the vertex.

Examples

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

To measure an angle with a protractor: (1) Place the center point on the vertex, (2) Align one ray with the $0°$ baseline, (3) Read where the second ray intersects the degree scale, choosing the scale that gives a reading less than $180°$ for acute and obtuse angles.

Examples