Angles

Circles

8. The circular spinner dial for a new board game is divided into 6 congruent sectors. What is the arc measure, in degrees, of each sector?

2015 December(72E) Math Question 8

13. In the figure below, G is the center of the circle, LK is a diameter, H lies on the circle, J lies outside the circle on LK, and JM is tangent to the circle at M. Which of the following angles or minor arcs has the greatest degree measure?

2015 April(73G) Math Question 13

14. You see a circle graph in a newspaper article about student employment, but no percentages are given for the sectors. You want to use the information contained in the graph in a report for your sociology class. You measure the central angle of the sector titled “work during the week” with your protractor, and it measures 144°. According to the circle graph and your measurement, the “work during the week” sector is what percent, to the nearest percent, of the circle graph?

Circle Graphs (Pie Charts)

2021 April(D05) Math Question 14

15. Antwan drew the circle graph below describing his time spent at school in 1 day. His teacher said that the numbers of hours listed were correct, but that the central angle measures for the sectors were not correct. What should be the central angle measure for the Core subjects sector?

2014 June(72C) Math Question 15

17. In the circle graph, what is the angle measure of the sector that represents the number of students who responded to the survey who selected Tennis?

2013 June(71C) Math Question 17

2019 June(72F) Math Question 18

2013 April(71G) Math Question 19

21. The Ferris wheel at a state fair has a radius of 60 feet, rotates at a constant speed, and completes 1 rotation in 4 minutes. How many degrees does the Ferris wheel rotate in 30 seconds?

2014 December(72G) Math Question 21

2019 April(B04) Math Question 22

26. Angle LJKL is shown below with the given lengths in coordinate units. What is the measure of LJKL in radians?

2016 December(74H) Math Question 26

26. A circle in the standard (x,y) coordinate plane has center C(-1,2) and passes through A(2,6). Line segment AB is a diameter of this circle. What are the coordinates of point B ?

2017 April(74F) Math Question 26

28. What angle measure, in radians, is equal to 30° ?

2021 June(D06) Math Question 28

2009 April(66F) Math Question 34

36. Jie asked 90 students to choose 1 favorite fruit from

2017 June(74C) Math Question 36

2010 June(68C) Math Question 37

2012 December(71A) Math Question 42

2019 April(Z15) Math Question 43

2011 June(69F) Math Question 43

44. Points O(0,0) and B(0,3) below lie in the standard (x,y) coordinate plane. The collection of all points such that each is twice as far from B as from 0 forms a circle. The point (V3,0) is 1 point on the circle. What are the coordinates of the center of that circle?

2015 April(73G) Math Question 44

2013 December(71E) Math Question 45

2010 June(68C) Math Question 46

2011 June(69F) Math Question 47

2009 June(67C) Math Question 48

48. A circle graph will be drawn with 3 sectors each representing the proportion of owners from Company A, B, and C who are 16 to 25 years old. What is the measure of the central angle for the Company A sector of the graph?

2020 December(D03) Math Question 48

2009 December(68A) Math Question 49

49. A circle, 2 chords. and some lengths, in centimeters, are shown in the figure below, which is not drawn to scale. What is the value of x ? (Note: When two chords intersect, the product of the lengths of the segments of one chord equals the product of the lengths of the segments of the other chord.)

2015 June(73C) Math Question 49

2012 April(70G) Math Question 50

2011 April(67F) Math Question 50

2010 April(68G) Math Question 51

52. From point A outside a circle and in the same plane as the circle, 2 rays are drawn tangent to the circle with the points of tangency labeled B and C, respectively. Segment BC is then drawn to form LABC. If A measures 70°, what is the measure of ABC ?

2016 April(73E) Math Question 52

2013 April(71G) Math Question 53

2012 December(71A) Math Question 53

53. Angle A measures radians from its initial side to its terminal side. Angle B has the same initial side and terminal side as Angle A. Which of the following measures could be that of Angle B ?

2013 June(71C) Math Question 53

2012 December(71A) Math Question 54

56. As shown below, 2 circular pulleys with centers 8 inches apart are connected with a tight belt. The belt wraps 2/3 of the way around the larger pulley, which has a radius of 5 inches, and 1/3 of the way around the smaller pulley, which has a radius of 1 inch. What is the exact length of the belt, in inches?

2014 April(71H) Math Question 56

2012 December(71A) Math Question 56

57. In the diagram below, chord EF is parallel to diameter AB. The length of EF is 10 inches and the length of AB is 14 inches. What is the distance, in inches, from C, the center of the circle, to D, the midpoint of EF ?

CirclesAnglesACT math questions

2015 December(72E) Math Question 8

2015 April(73G) Math Question 13