Sum = 180°: Challenge & Extension
Mathematics
GCSE Foundation
12 questions
~24 mins
1 views0 downloads
About This Worksheet
A worksheet exploring the fundamental rule that the interior angles of a triangle sum to 180°, including practice, problem solving, real-world applications, and extension questions.
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Sum = 180°: Challenge & Extension
Subject: MathematicsGrade: GCSE Foundation
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Untitled Worksheet
Grade GCSE Foundation
A
Practice Questions
Answer all questions. Show your working in the grid spaces provided.
1.
Calculate the third angle of a triangle if two angles measure 65° and 45°.
[2 marks]2.
Find the measure of an exterior angle of a triangle if one interior angle is 50° and the adjacent interior angle is 60°.
[2 marks]3.
In a triangle, the angles are in the ratio 2:3:5. Find the measure of the largest angle.
[3 marks]4.
Construct a triangle where one angle is 50°, another is 60°, and the third is found using the angle sum property. Use the grid to draw accurately.
[3 marks]5.
Plot the graph of y=2x and identify the points where the line intersects the grid within the first quadrant. (This involves drawing on the grid).
[3 marks]B
Problem Solving & Reasoning
Answer all questions clearly, showing detailed reasoning and calculations.
1.
A triangle has one angle measuring 80°. The second angle is twice the third. Find all angles of the triangle.
[4 marks]2.
A triangle has angles A, B, and C with A = 45°. Angle B is supplementary to angle C. Find the measures of B and C.
[4 marks]C
Real-world Applications
Solve these practical problems involving angle sums in triangles.
1.
A scaffold is built in the shape of a triangle with two angles measuring 35° and 55°. What is the measure of the third angle? Explain how this relates to the angle sum property.
[3 marks]D
Challenge & Extension
Attempt these more complex problems to deepen your understanding.
1.
Prove that in any equilateral triangle, each angle measures 60° using the angle sum property.
[4 marks]2.
Given a triangle with angles 2x + 10°, 3x, and x + 20°, find x and the measures of all angles.
[4 marks]E
Mixed Review & Error Analysis
Solve these questions and identify common mistakes made in angle calculations.
1.
A student claims that if two angles in a triangle are each 75°, the third must be 30°. Is this correct? Explain and correct the mistake if necessary.
[3 marks]2.
A triangle has angles 90°, x, and 2x. Find x and identify the error if the student says the angles sum to 200°.
[3 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)
- • Swap topics (Harry Potter → Macbeth)
- • Add more questions (10 → 15)
- • Adjust difficulty
Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet