Angles

2020 July(C01) Math Question 1

2010 April(68G) Math Question 1

1. In the figure below, C is on BD, ∠BAC measures 40°, and ∠ABC measures 110°. What is the measure of ∠ACD?

Triangle's exterior angle

2021 June(D06) Math Question 1

2019 December(C03) Math Question 2

2. The degree measures of the 3 angles of the triangle below are expressed in terms of x. What is the value of x ?

Sum of angles of a triangle

2021 December(E23) Math Question 2

In the figure below, parallel lines m and n are cut by transversal line t, and 2 angle measures are given. What is the value of x?

2023 April(F11) Math Question 2

In the figure below, C is on BD, ∠BAC measures 35°, and ∠ABC measures 95°. What is the measure of ∠ACD?

2024 April(Z13) Math Question 2

3.In the figure below, C is on BD, LBAC measures 42~,
and LABC measures 108°. What is the measure of
LACD?

2019 June(B02) Math Question 3

3. In the figure below, C lies on AD, the measure of ZBAC is 65°, the measure of ZBCD is 100°, and the measure of LABC is x°. What is the value of x ?

2016 December(74H) Math Question 3

4. In the figure below, QRS is equilateral, side QR is bisected by T, and side QS is bisected by U. What is the degree measure of TUS ?

2015 June(73C) Math Question 4

2012 April(70G) Math Question 4

2010 June(68C) Math Question 4

4. Three line segments intersect as shown in the figure below, forming angles with measures of 150°, 40°, and x°, respectively. What is the value of x ?

2018 April(A09) Math Question 4

2017 December(A10) Math Question 4

4. In the figure below, ∠QPR measures 40°, ∠PQR measures 105°, and points Q, R, and S are collinear. What is the measure of ∠PRS ?

2014 April(71H) Math Question 4

2020 June(C02) Math Question 5

5. In the trapezoid below, AB is parallel to DC. What is the measure of ∠C ?

2021 June(D06) Math Question 5

6. In AACD below, B is on AC, E is on AD, the measure of LCAD is 28°, and AD is perpendicular to both BE and CD. What is the measure of ZCBE ?

2017 June(74C) Math Question 6

2019 June(72F) Math Question 6

2010 April(68G) Math Question 6

6. In AABC, the sum of the measures of LA and LB is 57°. What is the measure of LC ?

2013 June(71C) Math Question 6

A fan has 3 evenly spaced blades of negligible thickness, as shown below. What is the measure of an angle between 2 blades?

2023 April(F11) Math Question 6

7. In parallelogram ABCD below, AC is a diagonal, the measure of %ABC is 40°, and the measure of LACD is 570. What is the measure of LCAD ?

2017 April(74F) Math Question 7

In △ABC, the measure of ∠B is 90°, and the measure of ∠A is 4 times the measure of ∠C. What is the measure of ∠C?

35 February(Z14) Math Question 7

2009 December(68A) Math Question 8

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

2013 December(71E) Math Question 9

2013 December(71E) Math Question 10

2009 April(66F) Math Question 10

10. The figure below shows lines AB and DC, line segments AT and BC, and 2 angle measures. What is the measure of ACB ?

2016 April(73E) Math Question 10

2011 April(67F) Math Question 11

2010 June(68C) Math Question 11

2009 June(67C) Math Question 11

A circle centered at F with a diameter of EB is shown below. The measure of ∠BFC is 18°, and the measure of ∠CFD is 108°. Angle ∠AFB is a right angle. What is the measure, in degrees, of arc DEA?

2024 December(H31) Math Question 11

12. In the figure below, C is the intersection of AD and BE. If it can be determined, what is the measure of LBAC ?

2014 June(72C) Math Question 12

12. In the figure below, AD intersects BG at C and is perpendicular to DE. Line DE intersects BG at F. Given that the measure of ZEFG is 25°, what is the measure of ZBCD ?

2018 June(A11) Math Question 12

In a certain isosceles triangle, the measure of the vertex angle is 34°. What is the measure of each of the 2 base angles?

2024 September(H11) Math Question 12

2010 June(68C) Math Question 13

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

2019 April(B04) Math Question 13

Numbered below are the 14 angles formed by parallel lines l and m and transversals p and q. Lines l, p, and q intersect at a single point. Which of the following congruence statements must be true?

2024 April(Z13) Math Question 13

2012 December(71A) Math Question 14

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

2012 April(70G) 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

In the figure below, point C is on AD, and 2 angle measures of △ABC are given. What is the measure of ∠BCD?

2024 June(G20) Math Question 15

2019 April(Z15) Math Question 16

2013 April(71G) Math Question 16

16. In the figure below, vertices D and F of ADEF lie on CG, the measure of LCDE is 148°, and the measure of EFG is 140°. What is the measure of DEF ?

2015 June(73C) Math Question 16

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

2009 December(68A) Math Question 17

2018 December(B05) Math Question 18

2019 June(72F) Math Question 18

2012 June(70C) Math Question 18

18. In the figure below, AE and BD intersect at C, and AB || DE. Which of the following angles must have the same measure as BAC?

2015 April(73G) Math Question 18

2010 December(69A) Math Question 18

19. In a plane, the distinct lines AB and CD intersect at A, where A is between C and D. The measure of ∠BAC is 47°. What is the measure of ∠BAD ?

2014 June(72C) Math Question 19

2013 April(71G) Math Question 19

In the figure below, B lies on AC, E lies on DF, AC ∥ DF, △EBF is isosceles with BE ≅ BF, and ∠CBF measures 34°. What is the measure of ∠BED?

2024 December(H31) Math Question 19

19. Loto begins at his back door and walks 8 yards east, 6 yards north, 12 yards east, and 5 yards north to the barn door. About how many yards less would he walk if he could walk directly from the back door to the barn door?

Pythagorean Theorem and Special Right Triangles

2021 April(Z04) Math Question 19

20. In the figure below, line m is perpendicular to line n, and
line p is parallel to line q. Lines m, n, and p intersect at a
single point Some angle measures are given. What is
the value of x ?

2019 June(B02) Math Question 20

20. In the figure below, parallel lines AB and CD are cut by transversals AC and BD that intersect at E. Two angle measures are given. What is the measure of ZABD ?

2015 December(72E) Math Question 20

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

21. In the figure below, A, B, C, and D lie on the circle centered at O. Which of the following does NOT appear in the figure?

Triangles

2021 April(Z04) Math Question 21

2019 June(72F) Math Question 22

22. For trapezoid ABCD shown below, AB || DC, the measures of the interior angles are distinct, and the measure of ∠D is x°. What is the degree measure of ∠A in terms of x ?

2014 June(72C) Math Question 22

2019 April(B04) Math Question 22

2019 April(Z15) Math Question 23

2019 December(C03) Math Question 23

2020 July(C01) Math Question 23

24. The circle shown below has diameter AD, and points B and C lie on the circle. The measure of ZCAD is 300, and the measure of minor arc CD is 60°. What is the measure of minor arc AC ?

2015 June(73C) Math Question 24

24. In Middletown, Main Street and Market Street are parallel to each other. Patrick Street intersects Market Street to form a 76° angle at the northeast corner, as shown in the figure below. What is the measure of the angle formed at the southeast corner of Main Street and Patrick Street? (Note: Each street is straight and has the same uniform width.)

2016 April(73E) Math Question 24

25. In nABC shown below, the measure of ∠A is 58°, and AB ≅ AC. What is the measure of ∠C ?

2021 April(Z04) Math Question 25

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

2012 June(70C) Math Question 27

27. Given that ∠R is the included angle between the 2 congruent sides of the isosceles triangle nRST, and the measure of ∠R is 50°, what is the measure of ∠S ?

2020 December(D03) Math Question 27

28. Distinct lines l and m intersect, forming 4 pairs of adjacent angles. Which of the following statements must be true about these 4 pairs of angles?

2014 April(71H) Math Question 28

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

2021 June(D06) Math Question 28

2013 April(71G) Math Question 31

2011 April(67F) Math Question 31

For 2 similar triangles, △ABC and △DEF, such that ∠A, ∠B, and ∠C correspond to ∠D, ∠E, and ∠F, respectively, how many feet long is DE when AB = 10 ft, BC = 12 ft, AC = 15 ft, and DF = 12 ft?

2023 September(G01) Math Question 31

In the figure below, line l is parallel to line m, and line n intersects the parallel lines. What is the value of x?

2024 September(H11) Math Question 32

33. In a plane, the distinct lines AB and CD intersect at A, where A is between C and D. The measure of BAC is 54°. What is the measure of BAD ?

2015 April(73G) Math Question 33

2012 April(70G) Math Question 34

2009 April(66F) Math Question 34

2020 July(C01) Math Question 35

35. In AABC, AB = 6 cm, AC = 12 cm, inLA = 600, and AC is the longest side. Which of the following statements about the measures of the angles in AABC must be true? (Note: mZX denotes the measure of angle X.)

2016 December(74H) Math Question 35

36. The measures of 4 interior angles of a pentagon are 70°, 100°, 110°, and 135°, respectively. What is the measure of the 5th interior angle?

2015 December(72E) Math Question 36

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

2017 June(74C) Math Question 36

2013 December(71E) Math Question 37

2010 June(68C) Math Question 37

In the figure shown below, AB ∥ DE, C is the intersection of AE and BD, ∠D is a right angle, and the given side lengths are in inches. What is the length of AC, in inches?

35 February(Z14) Math Question 37

2019 April(B04) Math Question 39

39. In the figure below, lines l and m are parallel. Lines a and b intersect l at the same point. What is the value of x?

2014 December(72G) Math Question 39

2010 April(68G) Math Question 39

39. A student is using a protractor, as shown below, to find the measures of the interior angles of nABC. Which of the following is closest to the degree measure of ∠C ?

2021 December(E23) Math Question 39

41. In the figure below, AD, BE, and CF all intersect at point Z. The measures of 2 angles are given. What is the measure of CZE ?

2014 December(72G) Math Question 41

In the figure below, k₁ and k₂ are parallel lines, and W and X are points on k₁ and k₂, respectively. In the same plane, point Z lies between k₁ and k₂, and some angle measures are given. What is the degree measure of ∠XZW?

2024 December(H31) Math Question 41

42. In the figure below, X and Z are on line m, and Y is on line 1. The exterior angle to AXYZ at Z measures 160°. One of the following statements gives sufficient . additional information to find the measure of Lb. Which one?

AnglesThere are 140 ACT math questions under Angles

Sub-topics

2020 July(C01) Math Question 1

2010 April(68G) Math Question 1