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E2.2 · Measure and construct angles to 360 degrees
Learn to measure and construct angles to 360 degrees through clear examples and targeted practice.
Ontario Grade 6 Mathematics
Spatial Sense
Read the turn from the starting ray
An angle describes a turn around a common endpoint called the vertex. A full turn is 360°, a straight turn is 180°, and a quarter turn is 90°. A protractor measures the turn between two rays; it does not measure the length of either ray. Always name the direction, clockwise or counterclockwise, because the same two ray positions can describe different turns. The figure below is generated from exact degree values, not from a photograph or a guess at the screen angle.
What you will learn
- Identify the vertex and starting ray.
- Measure a counterclockwise turn to 360°.
- Compare clockwise and counterclockwise turns.
Set up a protractor
Place the centre mark at the vertex. Align its zero-degree line with the starting ray. Choose the scale that begins at zero on that ray; reading the opposite scale is a frequent source of errors. If a ray is too short, extend it with a straightedge without moving the vertex.
Measure the intended direction
Start with a ray at 0° pointing right. Turning counterclockwise to 120° gives a 120° angle, larger than a right angle but smaller than a straight angle. The other route clockwise reaches the same ending ray after 240°. These are different turns, even though the rays coincide at the end.
Construct and check
To draw 120°, make the first ray, mark 120° on the correct protractor scale, and draw a second ray through the mark. Check that 120° + 240° = 360°. State the direction in your explanation so a reader knows which turn is intended.
Worked example
A 120-degree counterclockwise turn
Starting with a ray pointing right at 0°, turn counterclockwise to 120°. What angle did you make, and what is the clockwise turn to the same ray?
The orange arc marks the counterclockwise turn from 0° to 120°. The opposite clockwise turn between the same rays is 240°.
- Choose the startThe rightward ray is the 0° reference.
- Read the turnThe ending ray is 120° counterclockwise from the start.
- Find the other turnA full turn is 360°, so clockwise travel is 360° − 120° = 240°.
Answer: The counterclockwise angle is 120°; the clockwise turn to the same ray is 240°.
Check: 120° + 240° = 360°, one full turn.
Common mistakes and how to avoid them
Reading 240° when the question asks for counterclockwise 120°.
Correction: Begin at the named starting ray and follow the stated direction before choosing the protractor scale.
Lesson summary
- The vertex is the common endpoint of two rays.
- Direction is part of the turn description.
- Opposite-direction turns to the same ray total 360°.
Check your understanding
Question 1
A counterclockwise turn is 75°. What clockwise turn reaches the same ray?
- 285°
- 75°
- 105°
- 360°
Show answer and explanation
285°
360° − 75° = 285°.
Key terms
- Vertex
- The common endpoint of an angle’s rays.
- Protractor
- A tool used to measure or construct angles in degrees.
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About this lesson and its review
Published by DoAssignment. This reviewed lesson follows Ontario Grade 6 Mathematics, expectation E2.2. It is a study resource, not an official curriculum publication.
Before publication, content is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability. Errors can still occur, so corrections are welcomed.