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.

Polygon Exterior Angles worksheet preview
Name:Date:

Polygon Exterior Angles

Practise identifying exterior angles of polygons and using the 360° total-turn rule to find unknown angles and side counts.

Core ideas

Choose the best answer, identify each true statement, or complete the rule.

1.When one exterior angle is taken at each vertex of a convex polygon, what is their total?
  • 180°
  • 360°
  • 540°
  • It depends on how many sides the polygon has
2.A regular decagon has ten equal exterior angles. What is the size of each exterior angle?
  • 18°
  • 36°
  • 45°
  • 144°
3.Select all statements that are true about polygon exterior angles.
  • An interior angle and its adjacent exterior angle add to 180°.
  • The exterior angles of a regular polygon are equal.
  • The exterior-angle total increases when a polygon has more sides.
  • Walking once around a convex polygon gives a total turn of 360°.

Find missing angles

Use the 360° total for a complete circuit around a polygon. Show your calculation where space is provided.

4.A quadrilateral has exterior angles of 78°, 104° and 91°. Calculate the fourth exterior angle.
5.Find one exterior angle of a regular 12-sided polygon.
6.Five exterior angles of a hexagon measure 48°, 72°, 59°, 86° and 67°. Find the sixth angle.
7.Match each regular polygon to the size of one exterior angle.
  • Regular pentagon
  • Regular hexagon
  • Regular octagon
  • Regular 15-sided polygon
  • 60°
  • 24°
  • 45°
  • 72°
8.Complete the rule: The of the exterior angles, taking one at each vertex of a , is always .
9.Complete the sentence: A full walk around the shape makes one complete .

Explain and extend

Use clear reasoning and include working for calculation questions.

10.Explain why the exterior angles of a convex polygon add to 360°, using the idea of turning as you travel around its sides.
11.Every exterior angle of a regular polygon is 20°. How many sides does the polygon have? Show how you know.
12.A regular polygon has n sides and each exterior angle is 30°. Write an equation using n and solve to find the number of sides.

3 printable pages

  • An illustrated convex polygon shows exterior angles and a complete 360° turn.

    Page 1

  • Polygon exterior angle multiple-choice, matching and missing-angle calculations.

    Page 2

  • Reasoning about the 360° exterior-angle rule and finding a regular polygon's side count.

    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