Each Angle: Error Analysis & Misconceptions
Mathematics
GCSE Foundation
13 questions
~26 mins
1 views0 downloads
About This Worksheet
A worksheet focusing on understanding and calculating each exterior angle of polygons, aimed at GCSE Foundation students. Includes common misconception analysis and multi-step reasoning.
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Each Angle: Error Analysis & Misconceptions
Subject: MathematicsGrade: GCSE Foundation
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Untitled Worksheet
Grade GCSE Foundation
A
Fluency & Practice
Answer all questions. Show your working in the grid spaces provided.
1.
Calculate the measure of each exterior angle of a regular octagon.
[2 marks]2.
A regular polygon has an exterior angle of 30 degrees. How many sides does this polygon have?
[2 marks]3.
Construct a triangle with sides such that one exterior angle measures 100 degrees. Label the interior and exterior angles at that vertex.
[3 marks]B
Problem Solving & Reasoning
Answer all questions. Show your detailed working.
1.
A regular decagon has an exterior angle of 36 degrees. If one exterior angle was mistakenly calculated as 45 degrees, what error was made? Explain and correct the mistake.
[3 marks]2.
A polygon has 15 sides. Calculate each exterior angle, then determine if it is possible for the polygon to be regular. Explain why or why not.
[3 marks]3.
A shape has an exterior angle of 80 degrees. If the interior angle is mistakenly calculated as 100 degrees, identify the error and provide the correct interior angle.
[3 marks]C
Real-world Applications
Answer all questions with clear reasoning.
1.
A fence surrounds a regular polygon-shaped garden with an exterior angle of 45 degrees at each corner. How many sides does this garden have? What is the total angle around the garden?
[3 marks]2.
A car wheel is designed as a regular polygon with exterior angles of 20 degrees each. Determine the number of sides the polygon has and discuss whether such a shape is feasible for a wheel.
[3 marks]D
Challenge & Extension
Attempt these challenging questions. Show your reasoning.
1.
A polygon's exterior angles are in the ratio 2:3:4:5. Find the measure of each exterior angle and determine the number of sides of the polygon.
[3 marks]2.
Construct an irregular polygon with one exterior angle of 60 degrees and two other exterior angles that sum to 120 degrees. Show all steps and label your angles.
[3 marks]E
Mixed Review & Error Analysis
Identify errors in the following student work and correct them.
1.
Student states: 'Since each exterior angle of a regular hexagon is 60 degrees, the interior angle must be 120 degrees.' Is this correct? Explain and correct if necessary.
[2 marks]2.
A student calculates the exterior angle of a regular polygon as 50 degrees and concludes it has 8 sides. Identify the mistake and find the correct number of sides.
[2 marks]3.
A shape has interior angles measured at 80 degrees each. The student claims it is a regular polygon. Is this possible? Why or why not? Correct the misconception.
[2 marks]Quick Actions
What is Remix?
Create a new worksheet based on this one. Change the grade level, topic, number of questions, or difficulty - then generate a fresh version.
- • Change grade level (Grade 6 → Grade 7)
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- • Add more questions (10 → 15)
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet