Vocabulary inscribed angle intercepted arc subtend.

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Vocabulary inscribed angle intercepted arc subtend

Example 1A: Finding Measures of Arcs and Inscribed Angles Find each measure. mPRU Inscribed  Thm. Substitute 118 for mPU.

Example 1B: Finding Measures of Arcs and Inscribed Angles Find each measure. mSP Inscribed  Thm. Substitute 27 for m SRP. Multiply both sides by 2.

Check It Out! Example 1a Find each measure. Inscribed  Thm. Substitute 135 for m ABC. Multiply both sides by 2.

Example 3A: Finding Angle Measures in Inscribed Triangles Find a. WZY is a right angle WZY is inscribed in a semicircle. mWZY = 90 Def of rt.  5a + 20 = 90 Substitute 5a + 20 for mWZY. 5a = 70 Subtract 20 from both sides. a = 14 Divide both sides by 5.

Check It Out! Example 3a Find z. 8z – 6 = 90 Substitute. ABC is a right angle ABC is inscribed in a semicircle. mABC = 90 Def of rt.  8z – 6 = 90 Substitute. 8z = 96 Add 6 to both sides. z = 12 Divide both sides by 8.

Example 4: Finding Angle Measures in Inscribed Quadrilaterals Find the angle measures of GHJK. Step 1 Find the value of b. mG + mJ = 180 GHJK is inscribed in a . 3b + 25 + 6b + 20 = 180 Substitute the given values. 9b + 45 = 180 Simplify. 9b = 135 Subtract 45 from both sides. b = 15 Divide both sides by 9.

Step 2 Find the measure of each angle. Example 4 Continued Step 2 Find the measure of each angle. mG = 3(15) + 25 = 70 Substitute 15 for b mJ = 6(15) + 20 = 110 in each expression. mK = 10(15) – 69 = 81 mH + mK = 180 H and K are supp. mH + 81 = 180 Substitute 81 for mK. mH = 99 Subtract 81 from both sides

Find the angle measures of JKLM. Check It Out! Example 4 Find the angle measures of JKLM. Step 1 Find the value of b. mM + mK = 180 JKLM is inscribed in a . 4x – 13 + 33 + 6x = 180 Substitute the given values. 10x + 20 = 180 Simplify. 10x = 160 Subtract 20 from both sides. x = 16 Divide both sides by 10.

Check It Out! Example 4 Continued Find the angle measures of JKLM. Step 2 Find the measure of each angle. mM = 4(16) – 13 = 51 mK = 33 + 6(16) = 129 mJ = 360 – 252 = 108

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

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°