1. Over Lesson 10–3 5-Minute Check 1 A.60 B.70 C.80 D.90

2. Over Lesson 10–3 5-Minute Check 2 A.40 B.45 C.50 D.55

3. Over Lesson 10–3 5-Minute Check 3 A.40 B.45 C.50 D.55

4. Over Lesson 10–3 5-Minute Check 4 A.40 B.30 C.25 D.22.5

5. Over Lesson 10–3 5-Minute Check 5 A.24.6 B.26.8 C.28.4 D.30.2

6. Then/Now You found measures of interior angles of polygons. Find measures of inscribed angles. Find measures of angles of inscribed polygons.

7. central angle Inscribed angle B C A D

8. Concept

9. Example 1 Use Inscribed Angles to Find Measures A. Find m  X. Answer: m  X = 43

10. Example 1 Use Inscribed Angles to Find Measures B. = 2(52) or 104

11. Example 1 A.47 B.54 C.94 D.188 A. Find m  C.

12. Example 1 A.47 B.64 C.94 D.96 B.

13. Concept

14. Example 2 Use Inscribed Angles to Find Measures ALGEBRA Find m  R.  R   S  R and  S both intercept. m  R  m  SDefinition of congruent angles 12x – 13= 9x + 2Substitution x= 5Simplify. Answer: So, m  R = 12(5) – 13 or 47.

15. Example 2 A.4 B.25 C.41 D.49 ALGEBRA Find m  I.

16. Concept

17. Example 4 Find Angle Measures in Inscribed Triangles ALGEBRA Find m  B. ΔABC is a right triangle because  C inscribes a semicircle. m  A + m  B + m  C= 180 Angle Sum Theorem (x + 4) + (8x – 4) + 90 = 180Substitution 9x + 90= 180Simplify. 9x= 90Subtract 90 from each side. x= 10Divide each side by 9. Answer: So, m  B = 8(10) – 4 or 76.

18. Example 4 A.8 B.16 C.22 D.28 ALGEBRA Find m  D.

19. Concept

20. Example 5 Find Angle Measures INSIGNIAS An insignia is an emblem that signifies rank, achievement, membership, and so on. The insignia shown is a quadrilateral inscribed in a circle. Find m  S and m  T.

21. Example 5 Find Angle Measures Since TSUV is inscribed in a circle, opposite angles are supplementary. m  S + m  V = 180 m  U + m  T = 180 m  S + 90 = 180(14x) + (8x + 4)= 180 m  S = 9022x + 4= 180 22x= 176 x= 8 Answer: So, m  S = 90 and m  T = 8(8) + 4 or 68.

22. Example 5 A.48 B.36 C.32 D.28 INSIGNIAS An insignia is an emblem that signifies rank, achievement, membership, and so on. The insignia shown is a quadrilateral inscribed in a circle. Find m  N.

23. Homework:  Finish the treasure hunt!

24. A poor leprechaun has lost his pot of gold. You and your partner have agreed to help him find it. Start by answering the questions listed below off the worksheet. As you solve, find each answer in the maze. Your path of correct answers must be connecting (the boxes may be touching diagonally as well). Find the pot of gold! Good luck!