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Mastering Inscribed Angles: Solving Problems & Finding Measures

Explore inscribed angles in circles, learn to find intercepted arcs, and solve angle problems using angle properties in this comprehensive guide. Understand the relationship between central and inscribed angles, and apply your knowledge to real-world examples. Enhance your skills in calculating angle measures in inscribed triangles and quadrilaterals.

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Mastering Inscribed Angles: Solving Problems & Finding Measures

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  1. 9-4 Learning Targets I will find the measure of an inscribed angle. I will use inscribed angles and their properties to solve problems.

  2. 9-4 Vocabulary inscribed angle intercepted arc subtend

  3. 9-4 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.

  4. 9-4 Remember: Central angles have the same measure as their intercepted arcs. Inscribed angles have measure that are one-half the measure of its intercepted arc.

  5. 9-4 Example 1A: Finding Measures of Arcs and Inscribed Angles Find mPRU.

  6. 9-4 mSP Example 1B: Finding Measures of Arcs and Inscribed Angles Find

  7. 9-4

  8. 9-4 Example 2: Hobby Application An art student turns in an abstract design for his art project. Find mDFA. mDFA = mDCF + mCDF = 115°

  9. 9-4

  10. 9-4 Example 3A: Finding Angle Measures in Inscribed Triangles Find a. 5a + 20 = 90 5a = 70 a = 14

  11. 9-4 mLJM = mLKM Example 3B: Finding Angle Measures in Inscribed Triangles Find mLJM. 5b – 7 = 3b 2b – 7 = 0 2b = 7 b = 3.5

  12. 9-4

  13. 9-4 Example 4: Finding Angle Measures in Inscribed Quadrilaterals Find the angle measures of GHJK. Step 1 Find the value of b.

  14. 9-4 Example 4 Continued Step 2 Find the measure of each angle.

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