1. **Identify and name given parts of the circle** - 1. $RT$: From the problem context, this corresponds to a radius (segment from center to point on circle) so answer is D. Radius. - 2. $SQ$: A chord is a segment joining two points on circle, answer is E. Chord. - 3. $EP$: From center to point on circle, radius again, D. - 4. $SQ$: Already chord, E. - 5. $SR$: Segment inside circle joining two points, chord, E. - 6. $\angle PES$: Angle at point $E$ formed by points $P$ and $S$, central angle, G. - 7. $\angle QSR$: Angle on circle with vertex on circumference, inscribed angle, H. - 8. $SPQ$: Arc from $S$ to $Q$ through $P$ inside circle; likely minor arc, C. - 9. $PS$: Segment intersecting circle at two points and extended; secant line, I. - 10. $PRQ$: Line touching circle at one point; tangent line, J. 2. **Find measures of angles/arcs given:** - We have $m\angle LAM=43^\circ$, $m\angle HAG=35^\circ$, $m\angle KAH=90^\circ$ (right angle). Angles around point $A$ sum to $360^\circ$. 11. $m\angle LAK = m\angle LAM + m\angle MAK = 43^\circ + 47^\circ = 90^\circ$ (using provided choices, $B=47^\circ$ fits). So answer is 90° (C). 12. $m\angle JAH = m\angle JAK + m\angle KAH = ? + 90^\circ$; since $m\angle HAG=35^\circ$, and $m\angle KAH = 90^\circ$, so $m\angle JAH$ is complementary, answer D=133° fits difference from 180° minus 47°. 13. $m\angle LAJ = m\angle LAM + m\angle MAJ = 43^\circ + 47^\circ = 90^\circ$, A=43° + B=47° choices. 14. $m\angle JAK = ?$, using relationship sums, 47° (B). 15. $m\angle KAM = 90^6^6 - 43^6 = 47^6$ (B). 16-20. Arcs measures use addition or difference of given angles: - 16. $mLK$ = D=133° - 17. $mJK$ = E=137° - 18. $mLMG$ = F=145° - 19. $mJH$= A=43° - 20. $mKLM$= B=47° 3. **Multiple choice answers:** 21. Major arc with central angle $86^6$ is $360^6 - 86^6 = 274^6$ so answer is A. 22. Angle on circle vertex with chords is inscribed angle, B. 23. Sum of central angles of circle with no common interior points is full circle, D=360°. 24. In cyclic quadrilateral, opposite angles sum to 180°, so $m\angle MIL=180^6 - 95^6=85^6$, answer B. 25. Diameter $AG$ means $m\angle ADG=90^6$. Given $m\angle DFG=65^6$, $mAD=115^6$, answer B. 4. **Refer to figure questions 26-30:** 26. Inscribed angle: A. $\angle CED$. 27. Angle intercepting arc $\overset{\frown}{CD}$: B. $\angle AED$. 28. Given $\angle BEC=110^6$, $m\angle BEA=70^6$, answer C. 29. Given $mGD=110^6$, $m\angle GBD=40^6$, answer B. 30. Given $m\angle CAF=60^6$, $mCF=120^6$, answer C. Final answers: 1. D 2. E 3. D 4. E 5. E 6. G 7. H 8. C 9. I 10. J 11. C 12. D 13. A 14. B 15. B 16. D 17. E 18. F 19. A 20. B 21. A 22. B 23. D 24. B 25. B 26. A 27. B 28. C 29. B 30. C