Two straight lines from the same point make an angle. The angle is the turn between them.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
The turn is measured in a unit.
Degree is the unit for measuring a turn. A full circle is 360 degrees.
A quarter turn
A quarter of a full turn is 90 degrees. That is a right angle, the corner of a square.
The arms are not the angle
Drawing the lines longer changes nothing. Only the turn between them counts.
An angle measures turning, not length
An angle is the amount of turn between two rays that share an endpoint. It measures rotation. That is why the length of the arms is irrelevant — extending both arms does not change how far you turned.
Why 360 degrees
A full turn is divided into 360 equal parts called degrees. The number 360 was chosen by ancient astronomers because it divides evenly by so many numbers — 2, 3, 4, 5, 6, 8, 9, 10, 12 and more. That convenience is why the convention survived.
Angles worth knowing by sight
A quarter turn is 90°, a half turn is 180°, a three-quarter turn is 270°, and a full turn is 360°. Knowing these lets you judge any angle roughly before measuring, which is how you catch a protractor read from the wrong scale.
The long-arms illusion
A drawing with long arms often looks like a bigger angle than one with short arms, even when the turn is identical. The eye is measuring the drawing, not the rotation. Whenever two angles are being compared, ignore the arms and look only at the opening.
Step 2: Try It Yourself
Stretch the arms and watch the number refuse to move.
45° is an acute angle.
Making the arms longer does not change the angle. The angle is the turn, not the arms.
Step 3: Watch an Example
One step at a time.
Watch Ana Test the Arms
Ana thinks a bigger drawing means a bigger angle.
- Step 1
She sets the turn to 40 degrees and stretches the arms out.
Step 4: Your Turn
Practice makes it stick.
The Corner
Problem 1 of 2
How many degrees is a right angle?
degrees
The Full Turn
Problem 2 of 2
How many degrees in a full turn all the way round?
degrees
Turns and Degrees
1 of 4
How many degrees in a half turn?
2 of 4
How many right angles in a full turn?
3 of 4
Does making the arms longer change the angle?
4 of 4
How many degrees in three quarters of a turn?
Step 5: Quick Check
Show what you know.
Question 1 of 2
How many degrees is a half turn?
Question 2 of 2
What is an angle?
What You Learned
- An angle is the turn between two lines from one point.
- It is measured in degrees. A full turn is 360.
- Longer arms do not make a bigger angle.