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LESSON THIRTY-ONE: WHAT’S YOUR ANGLE?

LESSON THIRTY-ONE: WHAT’S YOUR ANGLE?. WHAT’S YOUR ANGLE?. Now that we have talked about inscribed figures, we can delve a bit more into angles within circles. WHAT’S YOUR ANGLE?. In a circle, there are infinitely many combinations of central angles.

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LESSON THIRTY-ONE: WHAT’S YOUR ANGLE?

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  1. LESSON THIRTY-ONE:WHAT’S YOUR ANGLE?

  2. WHAT’S YOUR ANGLE? • Now that we have talked about inscribed figures, we can delve a bit more into angles within circles.

  3. WHAT’S YOUR ANGLE? • In a circle, there are infinitely many combinations of central angles. • This is an angle whose vertex is the center of a circle.

  4. WHAT’S YOUR ANGLE? • The two arcs that are created when a circle is divided by a central angle are called the major arc and minor arc.

  5. WHAT’S YOUR ANGLE? • The minor arc is the one on the interior of the smaller central angle. • This one has been labeled for you. A B X C

  6. WHAT’S YOUR ANGLE? • The major arc is the one on the exterior of the smaller central angle. • Draw the arc on this circle below! A B X C

  7. WHAT’S YOUR ANGLE? • When naming the minor arc we need only two letters. • The minor arc below could be named AB or BA. A B X C

  8. WHAT’S YOUR ANGLE? • The major arcs however, need three letters to be accurately labeled. • ACB or BCA could be names for the arc below. A B X C

  9. WHAT’S YOUR ANGLE? • The angle of the major and minor arc will always be equal to thecentral angle which creates them.

  10. WHAT’S YOUR ANGLE? • When given one, you can find the other by simply, subtracting the measure from 360. • Furthermore, you can find the sum of two non-overlapping arcs by simply adding their measures.

  11. WHAT’S YOUR ANGLE? • Sometimes, a circle be divided directly in half. • The result is two semicircles. • All of these have a measure of 180. • You may apply the same principles we just discussed to semicircles.

  12. WHAT’S YOUR ANGLE? • For example, let’s see if we can find arc AC below. A X C 210

  13. WHAT’S YOUR ANGLE? • What about arc AB? A 42 B X C

  14. WHAT’S YOUR ANGLE? • Aside from central angles, there are also inscribed angles. • This is an angle whose vertex is on the circle.

  15. WHAT’S YOUR ANGLE? • How do you suppose central angles and inscribed angles are related?

  16. WHAT’S YOUR ANGLE? • The measure of the inscribed angle will be half of the included arc measure. • Furthermore, if two inscribed angle intercept the same arc, then they are congruent. • Also, an inscribed angle that intercepts a semicircle is a right angle.

  17. WHAT’S YOUR ANGLE? • We will be able to use this information to solve all kinds of problems. • See if you can find arcs AB and AC B C 40 A

  18. WHAT’S YOUR ANGLE? • See if you can find arcs CA, BC and AB below. • HINT: You may have to draw on some old knowledge. B 45 C 60 A

  19. WHAT’S YOUR ANGLE? • Try this…find the central angle! B C 70 A

  20. WHAT’S YOUR ANGLE? • It will help you as you do these problems to fill in bits of the circle as you go! • You might crack the code without even really knowing it!

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