An angle is formed by two rays that share the same endpoint, called the vertex. It is measured in degrees by how far one ray is turned from the other. A right angle measures 90 degrees, a straight angle measures 180 degrees, and one full turn is 360 degrees.
An angle is two rays from one vertex. Its size is the turn between the rays, measured in degrees, so a right angle is a quarter turn and a straight angle is a half turn.
Formal definition and notation
An angle is the figure formed by two rays, its sides, with a common endpoint, its vertex. Its measure is the fraction of a full circle that one side turns to reach the other, centered at the vertex. A full turn is 360°, so an angle that turns through 1360 of a circle measures 1°. The angle with vertex B and sides through A and C is written ∠ ABC.
Symbol
Read it as
Meaning
∠ ABC
angle A B C
the angle with vertex B; the vertex letter is always in the middle
Angles that make a straight line add to 180°, and angles that make a right angle add to 90°. Use these facts to find a missing angle.
Try it: turn the ray
Interactive
Drag the moving ray, or focus it and use the arrow keys (hold Shift for bigger steps). Watch the measure and the angle type change at 90 and 180 degrees.
This interactive needs JavaScript. The worked examples below show the same ideas step by step.
Angle examples, step by step
Example 1: Split a right angle
Warm-up
Ray BD splits the right angle∠ ABC into two angles. If ∠ ABD = 34°, find ∠ DBC.
A right angle measures 90°.
The two parts add up to the whole: ∠ ABD + ∠ DBC = 90°.
Subtract: 90° − 34° = 56°.
Answer:∠ DBC = 56°.
Example 2: Angles on a straight line
Core
Two angles sit side by side on a straight line. One measures 118°. What does the other measure, and what type of angle is it?
The vertex is the single point where the two sides meet; the angle is the whole figure and its opening. One vertex can belong to several angles.
Anglevs.Degree (temperature)
Angle degrees measure turn, with 360° in a full circle. Temperature degrees measure heat on a thermometer. They share a name and a symbol, nothing else.
Quick check: 3 questions
Question 1 of 3
What type of angle measures 95°?
Show answer and explanation
Answer: C.95° is more than 90° and less than 180°, so it is obtuse. Acute angles are under 90°, a right angle is exactly 90°, and a straight angle is exactly 180°.
Question 2 of 3
Two angles form a straight line. One is 47°. What is the other?
Show answer and explanation
Answer: A. Angles on a straight line add to 180°: 180° − 47° = 133°. Choice B subtracts from 90° (that is the complement), and choice C subtracts from 360°.
Question 3 of 3
Which change makes an angle larger?
Show answer and explanation
Answer: D. An angle’s size is the amount of turn between its sides. Longer sides, a new position or a bigger dot leave that turn unchanged.
Angle: frequently asked questions
What are the types of angles?
Angles are named by size. An acute angle is less than 90°, a right angle is exactly 90°, an obtuse angle is between 90° and 180°, a straight angle is exactly 180°, and a reflex angle is between 180° and 360°. A full turn, 360°, is sometimes called a full or complete angle.
How do you measure an angle?
Use a protractor. Put its center point on the vertex and line up the 0 mark with one side of the angle. Follow the scale that starts at 0 on that side until you reach the other side, and read the number of degrees. Estimate first: if the opening is narrower than a square corner, the answer must be under 90 degrees.
Can an angle be more than 180 degrees?
Yes. An angle between 180° and 360° is called a reflex angle. Two rays from one vertex always make two angles that add to 360°: if the smaller one is 100°, the reflex angle around the outside is 260°. Unless a problem says otherwise, ‘the angle’ means the smaller one.
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