National 5 Maths
Angles in Shapes
Course content
- Applying the properties of shapes to determine an angle.
- The working will involve at least two steps.
- The shapes could be triangles, quadrilaterals , other polygons or circles.
- Circle questions could involve the relationship between the centre, a chord and a perpendicular bisector.
Quadrilateral
A two-dimensional shape with four edges.
Examples: square, rectangle, rhombus, parallelogram, trapezium, kite, etc.
Polygon
A two-dimensional shape with straight edges.
Examples: triangle, quadrilateral, pentagon, hexagon, heptagon, octagon, nonagon etc.
The word polygon isn't often used to refer to triangles or quadrilaterals . It usually implies at least five sides.
Textbook page references
- Zeta National 5+ Maths pp.181-188
- TeeJay Maths N5 Book 4+ pp.139-146
- Leckie National 5 Maths pp.218-237
Key ideas
- The sum of the three angles in any triangle is 180°.
- The sum of the four angles in any quadrilateral is 360°.
- The sum of the exterior angles of any polygon is 360°.
- The angle between a radius and the corresponding tangent to a circle is 90°.
- When a triangle is formed inside a semicircle, the angle at the point not on the diameter is always 90°.
N5 Maths revision course
National5.com self-study courseSave £10 with discount code 'Maths.scot'
Example 1 (non-calculator)
Calculate the size of each angle inside a regular octagon.
Example 2 (non-calculator)
SQA National 5 Maths 2015 P1 Q3
AC is a tangent to the circle, centre O, with point of contact B.
DE is a diameter of the circle and F is a point on the circumference.
Angle ABD is 77° and angle DEF is 64°.
Calculate the size of angle BDF.
Recommended student book
Zeta Maths: National 5 Maths TextbookBest price, direct from the publisher
Example 3 (calculator)
SQA National 5 Maths 2016 P2 Q5
The diagram below shows a circle, centre O.
• AB and CB are tangents to the circle.
• AC and ED are parallel.
• Angle AOD is 143°.
Calculate the size of angle ABC.
Example 4 (non-calculator)
SQA National 5 Maths 2017 P1 Q9
In the diagram shown below:
• ABE is a tangent to the circle centre O
• Angle DBE is 58°
Calculate the size of angle CAB.
Recommended revision guides
How to Pass National 5 MathsBrightRED N5 Maths Study Guide
Example 5 (non-calculator)
SQA National 5 Maths 2022 P1 Q4
The diagram below shows a circle with centre O.
AB is a tangent to the circle at the point C.
CD is a diameter of the circle.
Angle EOD is 68°.
Calculate the size of angle ACE.
Example 6 (calculator)
SQA National 5 Maths 2023 P2 Q5
A logo consists of an H shape and a regular decagon.
The diagram represents the logo.
Calculate the size of the shaded angle.
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Past paper questions
• All past paper questions by topic |
Angles in polygons: • 2018 Paper 1 Q9 • 2019 Paper 1 Q11 (also circle) • 2023 Paper 2 Q5 |
Angles in circles: • 2015 Paper 1 Q3 • 2016 Paper 2 Q5 • 2017 Paper 1 Q9 • 2019 Paper 1 Q11 (also polygon) • 2021 Paper 1 Q4 • 2022 Paper 1 Q4 • 2024 Paper 1 Q10 |
Other great resources
Videos - Larbert High School 1. Angles in polygons 2. Tangents to circles 3. Isosceles triangles in circles |
Video - Mr Graham Maths Angles in circles |
PowerPoint - MathsRevision.com |
Lesson notes - Maths 777 1. Angles in polygons 2. Angles in circles 3. Pythagoras and trig in circles |
Worked examples - Maths Mutt |
Revision notes - BBC Bitesize 1. Triangles 2. Quadrilaterals 3. Polygons 4. Circles |
Worksheet - Brannock HS Pythagoras in circles (Answers) |
Exercises - Larkhall Academy Pages 1-21 Ex 1-5 (no answers) |
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