Free Grade 3 Introducing Angles Around a Point Lessons
Free Grade 3 lessons for Introducing Angles Around a Point: 12 real questions with a full answer key and worked solutions. Angles on a straight line add to 180°, around a point to 360°, and inside a triangle to 180°. A polygon with n sides has interior angles adding to (n − 2) × 180°.
Free
Higher
25 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify introducing angles around a point
Identify introducing angles around a point accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain introducing angles around a point
Explain introducing angles around a point accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing angles around a point
Calculate introducing angles around a point accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing angles around a point
Compare introducing angles around a point accurately in a familiar context.
Assessed by: Exit ticket of four short items
Prerequisites
Close these gaps first — each has its own free lesson, worksheet and quiz.
How Introducing Angles Around a Point works
Angles on a straight line add to 180°, around a point to 360°, and inside a triangle to 180°. A polygon with n sides has interior angles adding to (n − 2) × 180°.
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.Two angles on a straight line. One is 81°. Find the other.[1]
- 2.Two angles on a straight line. One is 27°. Find the other.[1]
- 3.Two angles on a straight line. One is 49°. Find the other.[1]
- 4.Two angles on a straight line. One is 119°. Find the other.[1]
- 5.A triangle has angles 40° and 112°. Find the third angle.[2]
- 6.A triangle has angles 45° and 74°. Find the third angle.[2]
- 7.A triangle has angles 20° and 82°. Find the third angle.[2]
- 8.A triangle has angles 90° and 32°. Find the third angle.[2]
- 9.Find the size of each interior angle of a regular 7-sided polygon.[3]
- 10.Find the size of each interior angle of a regular 8-sided polygon.[3]
- 11.Find the size of each interior angle of a regular 9-sided polygon.[3]
- 12.Find the size of each interior angle of a regular 5-sided polygon.[3]
Show answers and working
1. 99°
Angles on a straight line add to 180°. 180 − 81 = 99°.
2. 153°
Angles on a straight line add to 180°. 180 − 27 = 153°.
3. 131°
Angles on a straight line add to 180°. 180 − 49 = 131°.
4. 61°
Angles on a straight line add to 180°. 180 − 119 = 61°.
5. 28°
Angles in a triangle add to 180°. 180 − 40 − 112 = 28°.
6. 61°
Angles in a triangle add to 180°. 180 − 45 − 74 = 61°.
7. 78°
Angles in a triangle add to 180°. 180 − 20 − 82 = 78°.
8. 58°
Angles in a triangle add to 180°. 180 − 90 − 32 = 58°.
9. 128.57°
Sum of interior angles = (7 − 2) × 180 = 900°. Each angle = 900 ÷ 7 = 128.57°.
10. 135°
Sum of interior angles = (8 − 2) × 180 = 1080°. Each angle = 1080 ÷ 8 = 135°.
11. 140°
Sum of interior angles = (9 − 2) × 180 = 1260°. Each angle = 1260 ÷ 9 = 140°.
12. 108°
Sum of interior angles = (5 − 2) × 180 = 540°. Each angle = 540 ÷ 5 = 108°.
Worked examples
Two angles on a straight line. One is 54°. Find the other.
- Angles on a straight line add to 180°.
- 180 − 54 = 126°.
- Answer: 126°
A triangle has angles 56° and 75°. Find the third angle.
- Angles in a triangle add to 180°.
- 180 − 56 − 75 = 49°.
- Answer: 49°
Find the size of each interior angle of a regular 6-sided polygon.
- Sum of interior angles = (6 − 2) × 180 = 720°.
- Each angle = 720 ÷ 6 = 120°.
- Answer: 120°
Interactive practice
Free, no account required — answer on screen or print it.
Common mistakes
What learners typically get wrong, and how to fix it.
Reads the wrong scale on a protractor.
Correction: Start from the 0 on the arm you are measuring from.
Uses 360° for a triangle.
Correction: Triangle = 180°, quadrilateral = 360°.
Teacher tips
- · Estimate the angle type before measuring.
Parent tips
- · Spot right angles around the house.
Real-life applications
- · Ramps, clock hands, building and design.
Assessment objectives
How mastery is evidenced, and which standards it maps to.
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Frequently asked
- Is this Grade 3 Introducing Angles Around a Point lesson really free?
- Yes. Every lessons on FreeMathWorksheet is free to use, print and share — no account, no paywall and no watermark.
- What should a learner already know before this?
- Start with Angles on a Straight Line. Each one has its own free lesson, worksheet and quiz.
- How is the lesson sequenced?
- Recognition first, then understanding, application, reasoning and finally mastery — the same ladder used across every free resource on the platform.
- What comes next after Introducing Angles Around a Point?
- Move on to Working with Angles Around a Point, Angles Around a Point in Context, Angles on a Straight Line, Vertically Opposite Angles, which build directly on this idea.
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