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Angles BTESSSBAT: measure angles, identify angles, find the internal and external angles of regular polygons and use angle theorems to solve problems
Key words acute obtuse rotation reflex internal external theorem opposite parallel corresponding alternate supplementary
Angle B  or angle ABC or angle CBA A C Which is the largest angle? B G B D F E I E H H
Types of angles Right angle acute 90° obtuse 180° reflex
External angle Internal angle
360° 540° 720° 1080°
360° 540° 180° in a triangle: 720° 1080°
360° ÷ 4 540° ÷ 5 90° 108° 720° ÷ 6 1080° ÷ 8 135° 120°
90° 72° 60° 45°
Now try these 1. A regular dodecagon has 12 sides. Find its internal angle. 2. A regular polygon has an external angle of 36° - how many sides does it have? What is its internal angle?
Angle theorems A theorem is a law that is always true. 360° Angles at a point add up to  87° 55° 133° 85°
Angles on a straight line add up to  180° 85° 35° 60°
X- angles: opposite angles are equal  110° 70° 70° 110°
X- angles: opposite angles are equal  100° In fact we only need to know one angle: 80° 80° 100°
Now try these
Angles using parallel lines F angles: Corresponding angles (a and b) are equal
Angles using parallel lines Z angles: alternate angles (c and d) are equal
Angles using parallel lines Supplementary angles (a and c) add up to 180°
Now try these

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Angles