Learning Targets I will find the measure of an inscribed angle. 9-4 Learning Targets I will find the measure of an inscribed angle. I will use inscribed angles and their properties to solve problems.
9-4 Vocabulary inscribed angle intercepted arc subtend
9-4 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. A chord or arc subtends an angle if its endpoints lie on the sides of the angle.
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.
Example 1A: Finding Measures of Arcs and Inscribed Angles 9-4 Example 1A: Finding Measures of Arcs and Inscribed Angles Find mPRU.
Example 1B: Finding Measures of Arcs and Inscribed Angles 9-4 Example 1B: Finding Measures of Arcs and Inscribed Angles Find mSP
9-4
Example 2: Hobby Application 9-4 Example 2: Hobby Application An art student turns in an abstract design for his art project. Find mDFA. mDFA = mDCF + mCDF = 115°
9-4
Example 3A: Finding Angle Measures in Inscribed Triangles 9-4 Example 3A: Finding Angle Measures in Inscribed Triangles Find a. WZY is a right angle mWZY = 90 5a + 20 = 90 5a = 70 a = 14
Example 3B: Finding Angle Measures in Inscribed Triangles 9-4 Example 3B: Finding Angle Measures in Inscribed Triangles Find mLJM. mLJM = mLKM 5b – 7 = 3b 2b – 7 = 0 2b = 7 b = 3.5 mLJM = 5(3.5) – 7 = 10.5
9-4
Example 4: Finding Angle Measures in Inscribed Quadrilaterals 9-4 Example 4: Finding Angle Measures in Inscribed Quadrilaterals Find the angle measures of GHJK. Step 1 Find the value of b. mG + mJ = 180 3b + 25 + 6b + 20 = 180 9b + 45 = 180 9b = 135 b = 15
Step 2 Find the measure of each angle. 9-4 Example 4 Continued Step 2 Find the measure of each angle. mG = 3(15) + 25 = 70 mJ = 6(15) + 20 = 110 . mK = 10(15) – 69 = 81 mH + mK = 180 mH + 81 = 180 mH = 99