Free Grade 3 Introducing Polygons Lessons
Free Grade 3 lessons for Introducing Polygons: 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
Core
35 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain introducing polygons
Explain introducing polygons accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing polygons
Calculate introducing polygons accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing polygons
Compare introducing polygons accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introducing polygons
Justify introducing polygons 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 Polygons 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 91°. Find the other.[1]
- 2.Two angles on a straight line. One is 90°. Find the other.[1]
- 3.Two angles on a straight line. One is 114°. Find the other.[1]
- 4.Two angles on a straight line. One is 61°. Find the other.[1]
- 5.A triangle has angles 80° and 69°. Find the third angle.[2]
- 6.A triangle has angles 65° and 76°. Find the third angle.[2]
- 7.A triangle has angles 82° and 28°. Find the third angle.[2]
- 8.A triangle has angles 66° and 71°. Find the third angle.[2]
- 9.Find the size of each interior angle of a regular 8-sided polygon.[3]
- 10.Find the size of each interior angle of a regular 6-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. 89°
Angles on a straight line add to 180°. 180 − 91 = 89°.
2. 90°
Angles on a straight line add to 180°. 180 − 90 = 90°.
3. 66°
Angles on a straight line add to 180°. 180 − 114 = 66°.
4. 119°
Angles on a straight line add to 180°. 180 − 61 = 119°.
5. 31°
Angles in a triangle add to 180°. 180 − 80 − 69 = 31°.
6. 39°
Angles in a triangle add to 180°. 180 − 65 − 76 = 39°.
7. 70°
Angles in a triangle add to 180°. 180 − 82 − 28 = 70°.
8. 43°
Angles in a triangle add to 180°. 180 − 66 − 71 = 43°.
9. 135°
Sum of interior angles = (8 − 2) × 180 = 1080°. Each angle = 1080 ÷ 8 = 135°.
10. 120°
Sum of interior angles = (6 − 2) × 180 = 720°. Each angle = 720 ÷ 6 = 120°.
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 160°. Find the other.
- Angles on a straight line add to 180°.
- 180 − 160 = 20°.
- Answer: 20°
A triangle has angles 83° and 49°. Find the third angle.
- Angles in a triangle add to 180°.
- 180 − 83 − 49 = 48°.
- Answer: 48°
Find the size of each interior angle of a regular 10-sided polygon.
- Sum of interior angles = (10 − 2) × 180 = 1440°.
- Each angle = 1440 ÷ 10 = 144°.
- Answer: 144°
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 Polygons 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 Circles. 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 Polygons?
- Move on to Working with Polygons, Polygons in Context, Triangles, Quadrilaterals, which build directly on this idea.
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