Example 1
Three angles of a quadrilateral are 70°, 100°, and 80°. Find the fourth angle.
- Add the given three angles: 70° + 100° + 80° = 250°.
- Subtract from total interior sum 360°: 360° - 250° = 110°.
Answer: 110°
📙 Class 8 maths · session 3 of 13 · 60 minutes · 🎁 free with an account
Understanding quadrilaterals
Greetings, hero! Captain Calc here to help you unlock the power of four-sided shapes called quadrilaterals.
🤖 Written with Google's Gemini AI. A second AI solved all 55 questions without seeing the answers, and both agree. One of our teachers has not read it yet, so if something looks wrong, please tell us.
A complete lesson · 60 minutes
Teach it, see it, practise it, all on this page.
Open this page with your learner and work down it, or press Teach this lesson to go through it one step at a time on a big screen. Every section has something to do.
- Warm-up3 min
- Warm-up games5 min
- Polygons and Interior Angle Sum8 min
- Exterior Angles of Polygons7 min
- Properties of Parallelograms7 min
- Special Parallelograms: Rhombus, Rectangle, and Square7 min
- Operation Polygon Shield6 min
- Parallelogram Power Grid5 min
- Special Shape Vault6 min
- Quiz5 min
- Set the project1 min
By the end you can
- Calculate the sum of interior angles for any polygon
- Use the exterior angle sum rule to find missing angles
- Identify and apply properties of parallelograms
- Distinguish special quadrilaterals like rhombuses, rectangles, and squares
Before you start
- Basic properties of triangles and parallel lines
- Solving simple linear equations in one variable
Have ready
- Ruler and pencil
- Notebook for scratch work
Class 8 · CBSE, ICSE and state boards
Warm-up · think first
A triangular shield has angles measuring 50° and 60°. What is the measure of the third angle?
Show the answer
70° because the angles of a triangle add up to 180° (180 - 50 - 60 = 70).
Teacher tip: Remind students that angle sum rules help us find unknown angles quickly.
🎮 Warm-up games · 5 quick games
Play with Captain Calc
Six minutes with Captain Calc. Vote, say why, then show the answer.
- Which shape does not belong with the others? (Square · Rectangle · Rhombus · Circle)
Answer: Circle does not belong because it is not a polygon made of straight line segments. - Would you rather calculate the interior angle sum of a 10-sided polygon or the exterior angle sum of a 100-sided polygon? (Interior sum of 10-sided polygon · Exterior sum of 100-sided polygon)
Answer: Exterior sum of a 100-sided polygon! The sum of exterior angles for any polygon is always 360°, so no calculation is needed. - The diagonals of a quadrilateral cut each other at right angles (90°). (Always · Sometimes · Never)
Answer: Sometimes. This is true for rhombuses and squares, but not for all general parallelograms or rectangles. - I am a quadrilateral. My opposite sides are parallel and all four of my sides are equal in length, but my angles are not 90°. What shape am I?
Answer: Rhombus - Why do engineers and builders use quadrilaterals and triangles when designing city gates and bridges?
Answer: Triangles provide rigidity, while quadrilaterals like rectangles give structure for doors, windows, and tiles.
Part 1 of 4 · learn, see, practise
Polygons and Interior Angle Sum
A polygon is a closed flat shape made of straight line segments. A polygon with 4 sides is called a quadrilateral.
To find the sum of interior angles of a polygon with n sides, use the formula (n - 2) × 180°.
For any quadrilateral with 4 sides, the sum of interior angles is always (4 - 2) × 180° = 360°.
Example 2
Find the sum of the interior angles of a polygon with 6 sides (a hexagon).
- Use formula (n - 2) × 180° with n = 6.
- Calculate (6 - 2) × 180° = 4 × 180° = 720°.
Answer: 720°
Practise it
Start with the warm-up and go as far as you can. The stretch questions are meant to be hard.
Warm-up
Warm-up
Core
Core
Stretch 🔥
Stretch 🔥
Answers (for the teacher)
- 360
- 90
- 80
- 540
- 36
- 5
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Make a free account to open the rest of this lesson
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Unlocking the rest of this lesson gives you:
- Part 2: Exterior Angles of Polygons, with practice at three levels
- Part 3: Properties of Parallelograms, with practice at three levels
- Part 4: Special Parallelograms: Rhombus, Rectangle, and Square, with practice at three levels
- Class activity 1: Operation Polygon Shield
- Class activity 2: Parallelogram Power Grid
- Class activity 3: Special Shape Vault
- A 10-question quiz
- After-class project: Quadrilateral Hero HQ Blueprint
- Homework and a printable practice sheet with answers
- Teach mode and the minute-by-minute teacher's plan
It takes a minute. Anyone under 13 signs up with a parent. The first 2 lessons of every course, every game and all maths practice stay free.
FAQ
Understanding quadrilaterals: questions
Is a square always a rectangle and a rhombus?
Yes! A square has four right angles (making it a rectangle) and four equal sides (making it a rhombus).
What is the difference between a convex and a concave quadrilateral?
A convex quadrilateral has all interior angles less than 180°, while a concave quadrilateral has at least one interior angle greater than 180°.
Why is the exterior angle sum always 360° for any polygon?
If you walk all the way around the outer boundary of any closed polygon, you make one full turn, which equals 360°.
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