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Understanding Angles in and Out of the Circle: Central Angles and Arc Relationships

This guide explores the relationships between angles and arcs in circles, highlighting key properties such as central angles, inscribed angles, and angles formed by tangents and secants. It provides examples with given angles and arcs, illustrating how to find missing angle measures using the relationships between arcs and angles—both inside and outside of the circle. Perfect for students looking to deepen their understanding of circle geometry and the connections between angles and arcs.

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Understanding Angles in and Out of the Circle: Central Angles and Arc Relationships

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  1. Angles in and out of the circle • OOUT IN

  2. What we know so far • Central angle = arc • Angle ON the circle = ½ arc

  3. Vertex is inside the circle A ARC B ANGLE D ARC C Looks like a PLUS sign!

  4. Ex. 1 Find m1. 93° A B 1 D C 113°

  5. Ex. 2 Find mQT. N Q 84º 92º M T

  6. Ex 3: Find x. 40o xo 120o

  7. Challenge: 55º 110º wº 100º yº zº xº

  8. Vertex is outside the circle C Negative (-) temperatures outside… ANGLE small ARC A D LARGE ARC B LARGE ARC LARGE ARC small ARC ANGLE small ARC ANGLE

  9. Ex. 5 Find m1. 1 15° A D 65° B

  10. Ex. 6 Find mAB. A 27° 70° B

  11. Ex. 7 Find m1. 260° 1

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