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The Great Angle Chase There are many different pathways that lead to the same destination. Here is just one of them …
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Aim: To write in the size of every angle.
J I L M N K O S P Q R T U G H 25 100 35
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Look for the angle between a tangent and a chord.
Locate the angles in the alternate segment. J I L M N K O S P Q R T U G H 25 100 35 25 25
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J I L M N K O S P Q R T U G H 25 100 35 25 25
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Look for angles in the same segment.
J I L M N K O S P Q R T U G H 25 100 35 25 35 25
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J I L M N K O S P Q R T U G H 25 100 35 25 35 25
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Look for angles standing on equal chords.
J I L M N K O S P Q R T U G H 25 100 35 25 25 25 35 25
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J I L M N K O S P Q R T U G H 25 100 35 25 25 25 35 25
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Look for right angles: G U P T K L J M I O H N Q S R
25 100 35 The angle between a tangent and a radius The angle in a semicircle 25 65 25 65 40 25 35 25
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G U P T K L J M I O H N Q S R 25 65 35 25 65 25 40 25 100 35
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Look for triangles: G U P T K L J M I O H N Q S R Angle sum 25 65
100 35 Angle sum 25 65 55 25 55 65 40 25 35 40 75 25
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Look for triangles: G U P T K L J M I O H N Q S R Angle sum 25 65
100 35 Angle sum 25 65 55 25 55 65 40 75 25 120 35 40 75 25
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Look for triangles: G U P T K L J M I O H N Q S R Angle sum
25 100 35 25 Angle sum Exterior angle 65 55 25 125 55 65 40 75 25 120 35 40 75 25
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Look for triangles: G U P T K L J M I O H N Q S R Angle sum
25 100 35 25 Angle sum Exterior angle 65 55 60 25 125 55 65 40 75 25 120 35 40 75 25
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Look for vertically opposite angles and angles at a point.
J I L M N K O S P Q R T U G H 25 100 35 25 65 120 60 55 125 60 25 120 125 55 65 40 105 75 75 60 25 105 80 120 120 100 60 80 35 40 75 25
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And there’s another triangle.
J I L M N K O S P Q R T U G H 25 100 35 25 65 120 60 55 15 125 60 25 120 125 55 65 40 105 75 75 60 25 105 80 120 120 100 60 80 35 40 75 25
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And then another pair of angles in the same segment.
J I L M N K O S P Q R T U G H 25 100 35 25 65 120 60 55 15 125 60 25 120 125 55 65 40 105 75 75 60 25 105 80 120 120 100 60 80 35 40 75 25 15
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Some more right angles. G U P T K L J M I O H N Q S R 25 100 35 25
65 40 120 60 55 15 125 60 25 120 125 55 65 40 105 75 75 60 25 105 80 120 120 100 60 80 35 40 75 25 75 15
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Aha! A cyclic quadrilateral.
J I L M N K O S P Q R T U G H 25 100 35 25 65 40 120 60 55 15 125 60 25 120 125 55 65 40 105 75 75 60 25 105 80 120 120 100 60 80 35 40 80 75 25 75 15
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More angles at a point. G U P T K L J M I O H N Q S R 25 100 35 25
65 40 120 60 55 15 125 60 25 120 125 55 65 40 105 75 75 60 25 105 80 120 120 100 60 80 100 35 40 80 80 75 100 25 75 15
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G U P T K L J M I O H N Q S R 25 100 35 25 65 40 120 60 55
15 125 60 25 120 125 55 65 40 105 75 75 60 25 105 80 120 120 100 60 80 100 35 40 80 80 75 100 25 75 15
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Another angle between a tangent and a chord.
J I L M N K O S P Q R T U G H 25 100 35 25 65 40 120 60 55 15 125 60 25 120 125 55 65 40 105 75 75 60 25 105 80 120 120 100 60 80 100 35 40 80 80 75 100 40 25 75 15
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A cyclic quadrilateral.
J I L M N K O S P Q R T U G H 25 100 35 25 65 40 120 60 55 15 125 60 25 120 125 55 65 40 105 75 75 60 25 105 80 120 120 100 60 80 100 35 40 80 80 75 100 40 65 25 75 15
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And we’re done! G U P T K L J M I O H N Q S R 25 100 35 25 65 40
120 60 55 15 125 60 25 120 125 55 65 40 105 75 75 60 25 105 80 120 120 100 60 80 100 35 40 80 80 75 100 40 65 25 75 15
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