Logic Masters · Ages 11 to 12
Angles in Polygons Word Problems
Find interior angles of polygons using the angle-sum rules. A Grade 7 geometry worksheet with answer keys.
The learning journey
Every activity is one step. Here is where this one fits.
- PlayLearn the idea in a game
- Practise(you are here)Lock it in on paper
- ReviewCome back and keep it sharp
- MasterTake on a harder challenge
- AchieveEarn a certificate
About Angles in Polygons Word Problems
Angles in Polygons Word Problems develops Grade 7 understanding of how the angles inside a polygon are governed by simple, beautiful rules. Each problem asks the student to find either the sum of the interior angles of a polygon with a given number of sides, using the rule that the sum is the number of sides minus two, multiplied by one hundred and eighty, or the size of each interior angle of a regular polygon, by dividing that sum equally. Calculating interior angles of polygons is a core Grade 7 geometry expectation across the US, UK, Canada and Australia, and it shows how a single relationship generalises from triangles and quadrilaterals to any polygon. Working through the problems builds both the calculation and the understanding of why the rule holds, that any polygon can be split into triangles. The numbers are chosen so that regular-polygon angles come out cleanly. The five levels vary the polygons so the worksheet stays fresh and reusable. Each page prints cleanly on a standard A4 sheet, and every level downloads with its own answer key giving each angle in degrees. There is no advertising and no sign-up. Use it to secure angle rules or alongside our geometry games for the same age range.
Common questions
- What rule is used?
- The interior angle sum equals (number of sides − 2) × 180°.
- What grade is this for?
- Grade 7 learners aged 11 to 12.
- Is an answer key included?
- Yes, every level gives each angle in degrees.
A hand for grown-ups
- Before you start
- Point out a few shapes in the room first. Geometry starts with noticing, and it is everywhere.
- While they work
- Encourage them to turn shapes around and look from different angles — literally, with a real object if there is one.
- Afterwards
- Go on a shape hunt around the house together. Naming real shapes cements the vocabulary.
- Watch out for
- Thinking a rotated square is a "diamond", or that size changes what a shape is. Turning a real cut-out shows it is the same shape.
- Away from the screen
- Spot shapes on a walk, build with blocks, fold paper into shapes. Talk about corners and sides.
Where to go next
Chosen by the skills this activity practises.