The Great Angle Chase There are many different

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The Great Angle Chase There are many different pathways that lead to the same

The Great Angle Chase There are many different pathways that lead to the same destination. Here is just one of them …

Aim: To write in the size of every angle. G U P 35 K

Aim: To write in the size of every angle. G U P 35 K 25 L J 100 I M O H T N Q S R

Look for the angle between a tangent and a chord. • Locate the angles

Look for the angle between a tangent and a chord. • Locate the angles in the alternate segment. G U 25 P 35 K 25 L J 100 M O I H T N Q S 25 R

G U 25 P 35 K 25 L J 100 M O I H

G U 25 P 35 K 25 L J 100 M O I H T N Q S 25 R

Look for angles in the same segment. G U 25 P 35 K 25

Look for angles in the same segment. G U 25 P 35 K 25 L J 100 M O I T 35 H N Q S 25 R

G U 25 P 35 K 25 L J 100 M O I T

G U 25 P 35 K 25 L J 100 M O I T 35 H N Q S 25 R

Look for angles standing on equal chords. G U 25 P 25 35 K

Look for angles standing on equal chords. G U 25 P 25 35 K 25 L 25 J 100 T M O I 35 H N Q S 25 R

G U 25 P 25 35 K 25 L 25 J 100 T M

G U 25 P 25 35 K 25 L 25 J 100 T M O I 35 H N Q S 25 R

Look for right angles: G U • • The angle between a tangent and

Look for right angles: G U • • The angle between a tangent and a radius 25 65 P The angle in a semicircle 25 40 35 K 25 L 65 25 J 100 T M O I 35 H N Q S 25 R

G U 25 65 P 25 40 35 K 25 L 65 25 J

G U 25 65 P 25 40 35 K 25 L 65 25 J 100 T M O I 35 H N Q S 25 R

Look for triangles: G U 25 65 Angle sum P 35 25 40 55

Look for triangles: G U 25 65 Angle sum P 35 25 40 55 K 25 L 25 J 100 Q M O I 35 40 H T 55 65 N 75 S 25 R

Look for triangles: G U 25 65 Angle sum P 35 25 40 55

Look for triangles: G U 25 65 Angle sum P 35 25 40 55 K 25 75 100 25 J Q 120 M O I 35 40 H L T 55 65 N 75 S 25 R

Look for triangles: G U • Angle sum • Exterior angle 25 65 P

Look for triangles: G U • Angle sum • Exterior angle 25 65 P 35 25 40 55 K 25 75 100 25 J Q 120 M O I 35 40 H 125 L T 55 65 N 75 S 25 R

Look for triangles: G U • Angle sum • Exterior angle 25 65 P

Look for triangles: G U • Angle sum • Exterior angle 25 65 P 35 25 40 60 25 75 100 55 K 25 J Q 120 M O I 35 40 H 125 L T 55 65 N 75 S 25 R

Look for vertically opposite angles and angles at a point. G U 25 65

Look for vertically opposite angles and angles at a point. G U 25 65 P 35 25 40 120 60 60 K 120 25 55 125 L 55 65 105 75 75 60 25 J 80 100 I 100 80 105 Q 120 M 120 O 60 35 40 H T N 75 S 25 R

And there’s another triangle. G U 25 65 P 25 40 35 15 25

And there’s another triangle. G U 25 65 P 25 40 35 15 25 120 60 60 K 120 55 125 L 55 65 105 75 75 60 25 J 80 100 I 100 80 105 Q 120 M 120 O 60 35 40 H T N 75 S 25 R

And then another pair of angles in the same segment. G U 25 65

And then another pair of angles in the same segment. G U 25 65 P 25 40 35 15 25 120 60 60 K 120 55 125 L 55 65 105 75 75 60 25 J 80 100 I 100 80 105 120 M 120 O 60 35 40 H Q T N 75 S 25 15 R

Some more right angles. G U 25 65 P 40 35 25 40 120

Some more right angles. G U 25 65 P 40 35 25 40 120 60 60 K 120 15 25 55 125 L 55 65 105 75 75 60 25 J 80 100 I 100 80 105 Q 120 M 120 O 60 35 40 H T N 75 S 25 75 15 R

Aha! A cyclic quadrilateral. G U 25 65 P 40 35 25 40 120

Aha! A cyclic quadrilateral. G U 25 65 P 40 35 25 40 120 60 60 K 120 15 25 55 125 L 55 65 105 75 75 60 25 J 80 100 I 100 80 105 Q 120 M 120 O 60 35 40 H T 80 75 N S 25 75 15 R

More angles at a point. G U 25 65 P 40 35 25 40

More angles at a point. G U 25 65 P 40 35 25 40 120 60 60 K 120 15 25 105 75 75 80 100 I 100 80 105 O 120 M 120 60 100 80 80 N 100 40 Q T 60 25 J H 55 125 L 55 65 75 35 S 25 75 15 R

G U 25 65 P 40 35 25 40 120 60 60 K 120

G U 25 65 P 40 35 25 40 120 60 60 K 120 15 25 105 75 75 80 100 I 100 80 105 O 120 M 120 60 100 80 80 N 100 40 Q T 60 25 J H 55 125 L 55 65 75 35 S 25 75 15 R

Another angle between a tangent and a chord. G U 25 65 P 40

Another angle between a tangent and a chord. G U 25 65 P 40 35 25 40 120 60 60 K 120 15 25 105 75 75 80 100 I 100 80 105 O 120 M 120 60 100 80 80 N 100 40 Q T 60 25 J H 55 125 L 55 65 75 35 40 S 25 75 15 R

A cyclic quadrilateral. G U 25 65 P 40 35 25 40 120 60

A cyclic quadrilateral. G U 25 65 P 40 35 25 40 120 60 60 K 120 15 25 105 75 75 80 100 I 100 80 105 O 120 M 120 60 100 80 80 N 100 40 Q 75 35 40 65 25 T 60 25 J H 55 125 L 55 65 75 15 R S

And we’re done! G U 25 65 P 40 35 25 40 120 60

And we’re done! G U 25 65 P 40 35 25 40 120 60 60 K 120 15 25 105 75 75 80 100 I 100 80 105 O 120 M 120 60 100 80 80 N 100 40 Q 75 35 40 65 25 T 60 25 J H 55 125 L 55 65 75 15 R S

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