GCSE Angles and Geometry Learning Resources

Explore a collection of educational resources on angles and geometry for GCSE students. Includes diagrams, laws of angles, quick exercises, information on polygons, and more. Enhance your understanding of exterior angles, interior angles, and regular polygons with visual aids and examples. Perfect for exam revision and practice.

• GCSE
• Angles
• Geometry
• Learning Resources
• Education

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1. GCSE: Angles and Geometry Dr J Frost (jfrost@tiffin.kingston.sch.uk) Last modified: 5th January 2014

2. Starter Copy the diagram, then determine x. 55 55 33 192 33 136 11 70 x 114 44 44 22 11 22 x = 66 ?

3. Laws of Angles a a a a a a Opposite angles ? Alternate angles ? Corresponding angles ? Bro Tip: When asked to give a justification in an exam for how you determined an angle, write one of the above NOT Z angles or F angles . You won t get the mark.

4. Quick Exercises Q1 Q2 74 a = 65 , b = 103 , c = 38 ? c b 93 a a 77 a = 87 , b = 74 ? 115 b Q3 Q4 The two squares are congruent. Q5 50 68 y c 150 x 85 70 a c = 20 ? ? x = 150 , y = 95 ? a = 136

5. Angles in Polygons An exterior angle of a polygon is an angle between the line extended from one side, and an adjacent side. Which of these are exterior angles of the polygon? NO ? YES ? ? NO

6. Angles in Polygons To defeat Kim Jon Il, Matt Damon must encircle his pentagonal palace. What angle does Matt Damon turn in total? 360 ? The sum of the exterior angles of any polygon is 360 . Click to Start Damonimation

7. Angles in Polygons If the pentagon is regular, then all the exterior angles are clearly the same. Therefore: Exterior angle of pentagon = 360 / 5 = 72 ? Interior angle of pentagon = 180 72 = 108 ?

8. Angles in Polygons Num Sides Name of Regular Polygon Exterior Angle Interior Angle ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 3 Triangle 120 60 4 Quadrilateral 90 90 5 Pentagon 72 108 6 Hexagon 60 120 7 Heptagon 51.4 128.6 8 Octagon 45 135 9 Nonagon 40 140 10 Decagon 36 144 Bonus Question: What is the largest number of sides a shape can have such that its interior angle is an integer? 360 sides. The interior angle will be 179 . ?

9. Angles in Polygons Example GCSE Question Interior angle of hexagon = 180 (360 /6) = 60 Interior angle of octagon = 180 (360 /8) = 135 x = 360 120 135 = 105 ?

10. Angles in Polygons Copy the diagram and answer. Given that B has interior angle 60: Interior angle of A = (360 60)/2 = 150 Exterior angle of A = 30 So A has 360 / 30 = 12 sides?

11. Sum of Interior Angles We know how to find the interior angle of a regular polygon. But can we find the total angle if the polygon is not regular? We could split the shape up into n 2 triangles. n sides Now noticing that the interior angles of each triangle form the interior angles of the overall polygon, the total interior angle must be 180(n 2) Total interior angle = 180(n 2) ?

12. Sum of Interior Angles Num Sides Name Sum of Interior Angles ? ? ? ? 3 Triangle 180 4 Quadrilateral 360 5 Pentagon 540 6 Hexagon 720

13. Quick Exercises Q1 Q2 Q3 50 110 85 75 100 110 a b 80 80 60 80 80 c ? ? ? a = 110 b = 260 c = 70 Q4 Q5 Q6 The sum of the interior angles of a polygon is 3600 . How many sides does it have? 22 ? 62 242 62 81 284 88 a a 67 b 86 69 a = 119 , b = 25 ? ? ? a = 100