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Angles and Circles

Enhance your notes with examples on angles and circles, including solutions for arc measurements, congruent angles, tangents, secants, and central angles. Explore how to calculate angles formed by tangents and secants with clear explanations and practice problems. Improve your understanding of geometry concepts with practical examples.

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Angles and Circles

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  1. Angles and Circles Add examples from these slides to your notes!!!

  2. EXAMPLE Solution: Arc RQ = 360 – 140 – 100 Arc RQ = 120o M<QPR = (1/2) 120 M<QPR = 60o

  3. Congruent Angles From same intercepted arc If arc AB = 1000 , then <1 = 500 and <2 = 500 because they both Intercept the SAME ARC.

  4. Tangent and Chord Angles Note: The angle is partially in the circle and out of the circle. The arc is from the tangent point to the other end of the chord. EXAMPLE

  5. Central Angles and Arcs

  6. Angles formed by tangents and secants The measure of an angle formed by: * the intersection of 2 tangents to a point outside a circle is ½ the difference of the measures of the intercepted arcs. *the intersection of 2 secants *the intersection of a tangent and a secant

  7. Angles formed by tangents and secants EXAMPLES

  8. Note: <1 and <2 are NOT central angles, so they don’t equal the arcs! EXAMPLE

  9. Try these problems before you check the solutions!

  10. 1. (3x+70)-(2x+30) = 40 2 (3x+70)-(2x+30) = 80 x+40 = 80 x = 40 Then: if x = 40, 2(40)+30 = 1100 3(40)+70 = 1900 so, Y = 360 - 110 - 190 = 600 2. (125)-(x) = 35 2 125 - x = 70 x = 55 Then: if x = 550, Y = 360 - 100 - 55 - 125 = 800 3. x = 180 - 80 (linear pair = 180) x = 100o Then: (120)+(y) = 100 2 120 + y = 200 y = 80o

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