Free Grade 3 Angles in Polygons in Context Worksheets
Free Grade 3 worksheets for Angles in Polygons in Context: 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
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain angles in polygons in context
Explain angles in polygons in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate angles in polygons in context
Calculate angles in polygons in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare angles in polygons in context
Compare angles in polygons in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify angles in polygons in context
Justify angles in polygons in context 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 Angles in Polygons in Context 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 146°. Find the other.[1]
- 2.Two angles on a straight line. One is 56°. Find the other.[1]
- 3.Two angles on a straight line. One is 131°. Find the other.[1]
- 4.Two angles on a straight line. One is 46°. Find the other.[1]
- 5.A triangle has angles 32° and 105°. Find the third angle.[2]
- 6.A triangle has angles 57° and 81°. Find the third angle.[2]
- 7.A triangle has angles 62° and 60°. Find the third angle.[2]
- 8.A triangle has angles 90° and 45°. Find the third angle.[2]
- 9.Find the size of each interior angle of a regular 10-sided polygon.[3]
- 10.Find the size of each interior angle of a regular 9-sided polygon.[3]
- 11.Find the size of each interior angle of a regular 6-sided polygon.[3]
- 12.Find the size of each interior angle of a regular 5-sided polygon.[3]
Show answers and working
1. 34°
Angles on a straight line add to 180°. 180 − 146 = 34°.
2. 124°
Angles on a straight line add to 180°. 180 − 56 = 124°.
3. 49°
Angles on a straight line add to 180°. 180 − 131 = 49°.
4. 134°
Angles on a straight line add to 180°. 180 − 46 = 134°.
5. 43°
Angles in a triangle add to 180°. 180 − 32 − 105 = 43°.
6. 42°
Angles in a triangle add to 180°. 180 − 57 − 81 = 42°.
7. 58°
Angles in a triangle add to 180°. 180 − 62 − 60 = 58°.
8. 45°
Angles in a triangle add to 180°. 180 − 90 − 45 = 45°.
9. 144°
Sum of interior angles = (10 − 2) × 180 = 1440°. Each angle = 1440 ÷ 10 = 144°.
10. 140°
Sum of interior angles = (9 − 2) × 180 = 1260°. Each angle = 1260 ÷ 9 = 140°.
11. 120°
Sum of interior angles = (6 − 2) × 180 = 720°. Each angle = 720 ÷ 6 = 120°.
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 62°. Find the other.
- Angles on a straight line add to 180°.
- 180 − 62 = 118°.
- Answer: 118°
A triangle has angles 83° and 57°. Find the third angle.
- Angles in a triangle add to 180°.
- 180 − 83 − 57 = 40°.
- Answer: 40°
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.
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Frequently asked
- Is this Grade 3 Angles in Polygons in Context 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 Working with Angles in Polygons, Introducing Angles in Polygons, Angles in Parallel Lines. 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 Angles in Polygons in Context?
- Move on to Angles on a Straight Line, Angles Around a Point, Vertically Opposite Angles, Angles in Parallel Lines, which build directly on this idea.
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