MathsFreePrintable
Polygon Exterior Angles
A free maths worksheet ready for your classroom. Open in Kuraplan to grab the print-ready PDF, customize it for your students, or generate a fresh version in seconds.
Name:Date:
Polygon Exterior Angles
A navigation robot follows the edges of polygon-shaped paths. Use exterior angles to work out how far it turns. Unless stated otherwise, use one exterior angle at each vertex, measured in the same direction. Show working for calculation questions.
Part A: The key idea
Use the idea of a full turn to reason about exterior angles.
1.A robot travels all the way around a polygon, turning once at each vertex in the same direction. What is the total of its turns?
- 180°
- 360°
- 540°
- It depends on the number of sides
2.For any convex polygon, one exterior angle at each vertex, measured consistently in the same direction, has a total of 360°.
TrueFalse
3.A regular pentagon has five equal exterior angles. Calculate the size of each exterior angle.
4.A robot turns through 74°, 86°, 105° and 38° at four vertices of a pentagonal path. Find the exterior angle at the fifth vertex.
Part B: Solve the route
Use 360° as the total exterior-angle sum. Remember: each interior angle and its adjacent exterior angle add to 180°.
5.A regular octagonal garden path has eight equal exterior angles. Work out the size of each exterior angle.
6.Each exterior angle of a regular polygon is 24°. Calculate each interior angle.
7.A regular polygon has an exterior angle of 30°. How many sides does it have? Show how you know.
8.Ana says, “A regular polygon with an exterior angle of 40° must have 9 sides.” Is she correct? Explain using a calculation.
9.The four exterior angles of a quadrilateral are in the ratio 2:3:4:3. Calculate all four angles.
10.Explain why the exterior angles of a convex polygon add to 360°. Use the robot’s journey around the path in your explanation.
3 printable pages
Page 1
Page 2
Page 3
About This Worksheet
Free in Kuraplan
Sign up free, grab the PDF, and customize it for your class.
Print-Ready
Formatted for standard paper. Clean layout, easy to read.
AI-Generated
Created with Kuraplan's AI, designed for real classroom use.
For Teachers & Parents
Use in classrooms, for homework, tutoring, or homeschool.
Need a custom version of this worksheet?
Kuraplan's AI generates custom worksheets in seconds — differentiated for every learner, aligned to your curriculum.
Generate Custom Worksheets — Free No credit card Curriculum-aligned Under 60 seconds
