Free Grade 3 Working with Triangles Lessons
Free Grade 3 lessons for Working with Triangles: 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 working with triangles
Explain working with triangles accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with triangles
Calculate working with triangles accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with triangles
Compare working with triangles accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify working with triangles
Justify working with triangles 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 Triangles 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 116°. Find the other.[1]
- 2.Two angles on a straight line. One is 32°. Find the other.[1]
- 3.Two angles on a straight line. One is 147°. Find the other.[1]
- 4.Two angles on a straight line. One is 115°. Find the other.[1]
- 5.A triangle has angles 80° and 37°. Find the third angle.[2]
- 6.A triangle has angles 61° and 85°. Find the third angle.[2]
- 7.A triangle has angles 73° and 72°. Find the third angle.[2]
- 8.A triangle has angles 36° and 41°. Find the third angle.[2]
- 9.Find the size of each interior angle of a regular 5-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 8-sided polygon.[3]
Show answers and working
1. 64°
Angles on a straight line add to 180°. 180 − 116 = 64°.
2. 148°
Angles on a straight line add to 180°. 180 − 32 = 148°.
3. 33°
Angles on a straight line add to 180°. 180 − 147 = 33°.
4. 65°
Angles on a straight line add to 180°. 180 − 115 = 65°.
5. 63°
Angles in a triangle add to 180°. 180 − 80 − 37 = 63°.
6. 34°
Angles in a triangle add to 180°. 180 − 61 − 85 = 34°.
7. 35°
Angles in a triangle add to 180°. 180 − 73 − 72 = 35°.
8. 103°
Angles in a triangle add to 180°. 180 − 36 − 41 = 103°.
9. 108°
Sum of interior angles = (5 − 2) × 180 = 540°. Each angle = 540 ÷ 5 = 108°.
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. 135°
Sum of interior angles = (8 − 2) × 180 = 1080°. Each angle = 1080 ÷ 8 = 135°.
Worked examples
Two angles on a straight line. One is 131°. Find the other.
- Angles on a straight line add to 180°.
- 180 − 131 = 49°.
- Answer: 49°
A triangle has angles 39° and 88°. Find the third angle.
- Angles in a triangle add to 180°.
- 180 − 39 − 88 = 53°.
- Answer: 53°
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.
Every free resource for Working with Triangles
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Frequently asked
- Is this Grade 3 Working with Triangles 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 Introducing Triangles, Angles. 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 Working with Triangles?
- Move on to Triangles in Context, Quadrilaterals, Circles, Polygons, which build directly on this idea.
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