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Inscribed Angles

Inscribed Angles. Section 10-4. An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle. An intercepted arc consists of endpoints that lie on the sides of an inscribed angle and all the points of the circle between them.

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Inscribed Angles

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  1. Inscribed Angles Section 10-4

  2. An inscribed angleis an angle whose vertex is on a circle and whose sides contain chords of the circle. • An intercepted arcconsists of endpoints that lie on the sides of an inscribed angle and all the points of the circle between them. • A chord or arc subtendsan angle if its endpoints lie on the sides of the angle.

  3. mSP Example: Finding Measures of Arcs and Inscribed Angles Find each measure. mPRU

  4. Example: Find each measure. mDAE

  5. Example: Finding Angle Measures in Inscribed Triangles Find a. a = 14

  6. Example: Finding Angle Measures in Inscribed Triangles Find mLJM. b = 3.5 Divide both sides by 2.

  7. Example: Find z. z = 12 Divide both sides by 8.

  8. Example: Find mEDF. x = 18 mEDF= 2(18) + 3 = 39°

  9. Draw a circle; divide it into 4 arcs (they do not have to be equal); draw the chord of each arc; investigate angle relationships

  10. Example: Finding Angle Measures in Inscribed Quadrilaterals Find the angle measures of GHJK.

  11. Lesson Quiz: Part I Find each measure. 1. RUS 2. a 25° 3

  12. Lesson Quiz: Part II 3. A manufacturer designs a circular ornament with lines of glitter as shown. Find mKJN. 130° 4. Find the angle measures of ABCD. mA = 95° mB = 85° mC = 85° mD = 95°

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