Primary 5 maths · Geometry · About 12 minutes
Use angles around a point
Locate the common vertex, the given lines and the complete turn being filled.
Start the interactive lesson →Open practice activity
What you will learn
- Use angles around a point
Models used: number sentences, stories, tables.
Before you start
Turn all the way back to the start
A quarter-turn takes you to a new direction.
A quarter-turn takes you to a new direction.
90°
A right-angle turn. Four quarter-turns bring you back to your starting direction.
90° + 90° + 90° + 90° = 360°
A complete turn around a point. The complete bar is the whole. Each labelled section is one part of it.
If 140° of the full turn is known, the rest must fill the remaining 220°.
360° − 140° = 220°
What did the picture help us see?
If 140° of the full turn is known, the rest must fill the remaining 220°.
Worked example: A new example, together
Angles 70° and x° make a full turn about a point. Find x.
| Known angle | Relationship |
|---|---|
| 70° | 360° total |
Use the marked relationship. Read each value with the heading above its column.
Locate the common vertex, the given lines and the complete turn being filled.
The component angles exactly fill 360 degrees.
Use the marked relationship Known angle Relationship 70° 360° total Use the marked relationship. Read each value with the heading above its column.
The complete turn here is 360°.
Use the marked relationship Known angle Relationship 70° 360° total Angles 70° and x° make a full turn about a point. Find x.
290 degrees
Use the marked relationship. Read each value with the heading above its column.
Subtract the known angle: 360 − 70.
Use the marked relationship Known angle Relationship 70° 360° total Use the marked relationship. Read each value with the heading above its column.
x = 290°.
Use the marked relationship Known angle Relationship 70° 360° total Use the marked relationship. Read each value with the heading above its column.
Check the result against the question we started with.
70 + 290 = 360°.
We found 290 degrees. The component angles exactly fill 360 degrees.
Use the marked relationship Known angle Relationship 70° 360° total
Common mistakes to discuss
- Stopping at a straight line. A full turn is 360°. Three angles about a point of 150° and 100° leave 110°.
Check your understanding
- Use angles around a point
- justify an unknown angle with the stated angle relationship
- check the answer against the original quantities and units
Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.
Try this lesson →Related Primary 5 lessons
- Use angles on a straight lineUse angles on a straight line · About 12 minutes
- Use vertically opposite anglesUse vertically opposite angles · About 12 minutes
- Find unknown anglesFind unknown angles · About 12 minutes
- Recognise triangle types and use the angle sum of a triangleRecognise triangle types and use the angle sum of a triangle · About 12 minutes
- Use parallelogram, rhombus and trapezium propertiesUse parallelogram, rhombus and trapezium properties · About 12 minutes
- Find unknown angles without adding linesFind unknown angles without adding lines · About 12 minutes