GCSE: Angles and Geometry Dr J Frost (jfrosttiffin.kingston.sch.uk) Last modified: 5th January 2014 Copy the diagram, then determine x. 11 x 22 11 22 136 33 33 114 44 44 192 55 55 70 x 66 ? a a a a a a Opposite angles
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Presentation Transcript
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GCSE: Angles and Geometry Dr J Frost (jfrost@tiffin.kingston.sch.uk) Last modified: 5th January 2014<br>
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Copy the diagram, then determine x. 11° x° 22° 11° 22° 136° 33° 33° 114° 44° 44° 192° 55° 55° 70° x = 66° ?<br>
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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. ? ? ?<br>
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74° 93° b a 115° a b° 77° c 70° 50° c 68° a The two squares are congruent. Q1 Q2 Q3 Q4 a = 87°, b = 74° a = 65°, b = 103°,
c = 38° c = 20° a = 136° ? ? ? ? Q5 150 85 y x x = 150°, y = 95° ?<br>
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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 ? ? ?<br>
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Click to Start Damonimation 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°. ?<br>
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If the pentagon is regular, then all the exterior angles are clearly the same. Therefore: Exterior angle of pentagon
= 360 / 5 = 72°
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°. ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?<br>
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Example GCSE Question Interior angle of hexagon = 180° – (360°/6) = 60°
Interior angle of octagon = 180° – (360°/8) = 135°
x = 360° – 120° – 135° = 105° ?<br>
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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 ?<br>
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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? n sides We could split the shape up into n – 2 triangles.
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) ?<br>
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? ? ? ?<br>
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80 80 a a = 110° 110 100 80 b 60 110 b = 260° 50 75 85 80 c = 70° c 62 242 81 a 69 284 62 a = 100° 88 67 86 a b a = 119°, b = 25° The sum of the interior angles of a polygon is 3600°. How many sides does it have?
22 Q1 Q2 Q3 Q4 Q5 Q6 ? ? ? ? ? ? ?<br>
