360°: Real-world Applications
Mathematics
GCSE Foundation
12 questions
~24 mins
1 views0 downloads
About This Worksheet
A worksheet exploring the concept of 360° in real-world contexts and problem-solving scenarios related to angles at a point.
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360°: Real-world Applications
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.
If three angles at a point are 85° and 120°, find the size of the remaining angle.
[2 marks]2.
Calculate the sum of four angles around a point if three are 95°, 110°, and 85°.
[3 marks]3.
A full rotation is 360°. If an angle is 240°, what is its supplementary angle at the same point?
[2 marks]B
Problem Solving & Reasoning
Answer all questions clearly, showing detailed working.
1.
A clock shows two hands forming an angle of 120°. If the minute hand has moved 20 minutes past the hour, what is the angle between the hour and minute hands?
[4 marks]2.
On a circular table, three people sit so that the angles between them are 100°, 130°, and the remaining angle. Find the largest possible angle between two people sitting opposite each other.
[4 marks]C
Real-world Applications
Solve the following contextual problems using your understanding of angles at a point.
1.
A bridge is constructed with multiple segments meeting at a joint. If four segments form angles of 90°, 85°, and 100° at the joint, what is the measure of the remaining angle needed for the angles to sum to 360°?
[2 marks]2.
In a roundabout, three roads meet, forming angles of 110°, 130°, and an unknown angle. What is the measure of the unknown angle?
[2 marks]D
Challenge & Extension
Attempt these advanced problems to extend your understanding.
1.
Construct an angle at a point where one angle is 150°, and the other two are equal. Calculate the measure of the equal angles.
[3 marks]2.
A circular platform has three sections separated by angles of 80°, 110°, and the remaining section. Find the measure of the last section.
[2 marks]E
Mixed Review
Answer a variety of questions to test your overall understanding of 360° at a point.
1.
If two angles at a point are 70° and 150°, what is the measure of the third angle?
[2 marks]2.
A pie chart shows 3 sectors with angles of 90°, 150°, and an unknown sector. What is the angle of the unknown sector?
[2 marks]F
Error Analysis
Review the common mistake and correct it.
1.
A student calculates an unknown angle at a point by subtracting the two known angles from 360°, but the answer they get is 235°. Identify the mistake and provide the correct answer.
[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)
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- • Add more questions (10 → 15)
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet