Free Grade 3 Working with Polygons Worksheets
Free Grade 3 worksheets for Working with 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
Stretch
15 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain working with polygons
Explain working with polygons accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with polygons
Calculate working with polygons accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with polygons
Compare working with polygons accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify working with polygons
Justify working with 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 Working with 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 79°. Find the other.[1]
- 2.Two angles on a straight line. One is 152°. Find the other.[1]
- 3.Two angles on a straight line. One is 134°. Find the other.[1]
- 4.Two angles on a straight line. One is 120°. Find the other.[1]
- 5.A triangle has angles 36° and 21°. Find the third angle.[2]
- 6.A triangle has angles 44° and 24°. Find the third angle.[2]
- 7.A triangle has angles 82° and 74°. Find the third angle.[2]
- 8.A triangle has angles 26° and 91°. 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 10-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. 101°
Angles on a straight line add to 180°. 180 − 79 = 101°.
2. 28°
Angles on a straight line add to 180°. 180 − 152 = 28°.
3. 46°
Angles on a straight line add to 180°. 180 − 134 = 46°.
4. 60°
Angles on a straight line add to 180°. 180 − 120 = 60°.
5. 123°
Angles in a triangle add to 180°. 180 − 36 − 21 = 123°.
6. 112°
Angles in a triangle add to 180°. 180 − 44 − 24 = 112°.
7. 24°
Angles in a triangle add to 180°. 180 − 82 − 74 = 24°.
8. 63°
Angles in a triangle add to 180°. 180 − 26 − 91 = 63°.
9. 128.57°
Sum of interior angles = (7 − 2) × 180 = 900°. Each angle = 900 ÷ 7 = 128.57°.
10. 144°
Sum of interior angles = (10 − 2) × 180 = 1440°. Each angle = 1440 ÷ 10 = 144°.
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 69°. Find the other.
- Angles on a straight line add to 180°.
- 180 − 69 = 111°.
- Answer: 111°
A triangle has angles 32° and 98°. Find the third angle.
- Angles in a triangle add to 180°.
- 180 − 32 − 98 = 50°.
- Answer: 50°
Find the size of each interior angle of a regular 8-sided polygon.
- Sum of interior angles = (8 − 2) × 180 = 1080°.
- Each angle = 1080 ÷ 8 = 135°.
- Answer: 135°
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.
Every free resource for Working with Polygons
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Frequently asked
- Is this Grade 3 Working with Polygons worksheet really free?
- Yes. Every worksheets 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 Introducing Polygons, Circles. Each one has its own free lesson, worksheet and quiz.
- How is the worksheet 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 Working with Polygons?
- Move on to Polygons in Context, Triangles, Quadrilaterals, Circles, which build directly on this idea.
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