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7.01 Review: Classifying and measuring angles


An angle is formed between two lines, rays, or segments whenever they intersect. We can think of an angle as a turn from one object to the other.

The most important angle in geometry is called a right angle, and represents a quarter of a turn around a circle. When two objects form a right angle, we say they are perpendicular. We draw a right angle using a small square rather than a circular arc:

Two perpendicular segments.

We draw all other angles with a circular arc. An angle that is smaller than a right angle is called an acute angle. Here are two:

Two right angles together form a straight angle:

Four right angles is the same as two straight angles, making a full revolution:

An angle that is larger than a right angle but smaller than a straight angle is called an obtuse angle. Here are two:

We met the last kind of angle in the previous lesson - a reflex angle is larger than a straight angle, but smaller than a full revolution. Here are two:

Angle types

Angles are a measure of turning. All angles can be compared to a right angle, representing a quarter turn.

Practice question

Question 1

Select the obtuse angle:

  1. Two rays that share a common endpoint having an angle of 180 degrees.


    Two line segments that share a common endpoint having an angle of 90 degrees.


    Two line segments that share a common endpoint having an angle more than 90 degrees but less than 180 degrees.


    Two line segments that share a common endpoint having an angle less than 90 degrees.


Measuring angles

We divide a full revolution up into $360$360 small turns called degrees, and write the unit using a small circle, like this: $360^\circ$360°.

Since $90$90 is one quarter of $360$360, we know that a right angle is exactly $90^\circ$90°. This circle has markings every $45^\circ$45°:

We can measure angles more precisely using a protractor, or an applet like this one:

This lets us associate numbers with the angle types we learned about above.

Angle size

A full revolution is made up of $360$360 degrees, a single degree is written $1^\circ$1°.

Angle type Angle size
Acute angle Larger than $0^\circ$0°, smaller than $90^\circ$90°.
Right angle $90^\circ$90°
Obtuse angle Larger than $90^\circ$90°, smaller than $180^\circ$180°.
Straight angle $180^\circ$180°
Reflex angle Larger than $180^\circ$180°, smaller than $360^\circ$360°.
Full revolution $360^\circ$360°


Practice question

Question 2

Select the angle that is closest to $120^\circ$120°:

  1. A small square indicates that the angle is a right angle.


    The angle is close to 135 degrees.


    The angle is close to 135 degrees.


    The angle is greater than 135 degrees but less than 180 degrees.




Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

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