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There is a circle with center M and two chords A C and T N. The distences between M and the two chords are equal. Find m \angle C A M.
Choices:
A:14
B:28
C:36
D:90
|
B
|
|
In the figure below, \angle A B C is intersected by parallel lines l and m at points A and C, respectively. What is the measure of \angle A B C? Express your answer in degrees.
Choices:
A:33
B:38
C:61
D:71
|
D
|
|
There are four rays with four different included angles. Find the value of x in the diagram.
Choices:
A:68
B:78
C:79
D:136
|
A
|
|
Two triangles X N M and X Z Y are similar with a shared vertex X. M N and Y Z are parallel. If X N = 6, X M = 2, and X Y = 10, find N Z.
Choices:
A:12
B:16
C:24
D:32
|
C
|
|
There is a right triangle with two angles 30 and 60 degrees. The length of hypotenuse is x and other sides are y and 21. Find y.
Choices:
A:21
B:21 \sqrt { 2 }
C:21 \sqrt { 3 }
D:42
|
C
|
|
Two triangles A B C and A E D are similar with a shared vertex A. B C and E D are parallel. Find C D if A C = x - 3, B E = 20, A B = 16, and C D = x + 5.
Choices:
A:32
B:35
C:36
D:40
|
D
|
|
Two small circles are inscribed to the biggest circle. The diameter of the biggest circle is 20. Find the area of the shaded region. Round to the nearest tenth.
Choices:
A:104.7
B:157.1
C:235.6
D:314.2
|
B
|
|
J K L M is a rectangle. M L P R is a rhombus. M L equals M R. \angle J M K \cong \angle R M P, m \angle J M K = 55, and m \angle M R P = 70. Find m \angle K M L.
Choices:
A:35
B:70
C:110
D:140
|
A
|
|
In rhombus A B C D, m \angle D A B = 2, m \angle A D C and C B = 6. D B and A C intersect at point E. Find m \angle A C D.
Choices:
A:45
B:60
C:90
D:180
|
B
|
|
Two triangles A B E and A C D are similar with a shared vertex A. B E and C D are parallel. Find A E if A B = 12, A C = 16, and E D = 5.
Choices:
A:12
B:15
C:16
D:20
|
B
|
|
In parallelogram M N P R, M P and R N intersect at Q. M N = 3x - 4. N P = 2y + 5. R P = 20. M R = 17.9. Find m \angle R N P.
Choices:
A:38
B:52
C:52
D:62
|
A
|
|
Three rays intersect at two points. Two shorter rays are parallel. Find y in the figure.
Choices:
A:5
B:6
C:7
D:8
|
B
|
|
In \odot P, the radius is 2 inches. \angle Q P T is 112 degrees, and \angle RPS is 130 degrees. Find the length of \widehat R S. Round to the nearest hundredth.
Choices:
A:2.27
B:3.91
C:4.54
D:7.82
|
C
|
|
In parallelogram A B C D, AD = 9 and A B = 6. Find m \angle A D C.
Choices:
A:42
B:52
C:72
D:128
|
D
|
|
The rectangle is inscribed into the circle with two sides 8 and 6 inches. Find the exact circumference of the circle.
Choices:
A:8 \pi
B:10 \pi
C:16 \pi
D:20 \pi
|
B
|
|
There are two right triangles D F E and A C B. Find D E.
Choices:
A:3
B:4
C:6
D:9
|
D
|
|
There is a parallelogram with two sides 20 and 12 cm. Find its perimeter. Round to the nearest tenth if necessary.
Choices:
A:60
B:62
C:64
D:66
|
C
|
|
In \odot O, the diameter is 14, and \angle A O B is 80 degrees. Find the length of \widehat A B. Round to the nearest hundredth.
Choices:
A:7.63
B:9.77
C:11.13
D:14.83
|
B
|
|
Find A B if \triangle A B C is an isosceles triangle with A B \cong B C.
Choices:
A:3
B:4
C:7
D:11
|
C
|
|
In \odot G, CE and AB are diameters. \angle A G D is a right angle and \angle A G C is 60 degrees. Find m \angle B G E.
Choices:
A:60
B:120
C:240
D:360
|
A
|
|
In the triangle, there are two angles as 60 and 55 degrees. Find x. Round the side measure to the nearest tenth.
Choices:
A:69.0
B:69.8
C:76.4
D:77.2
|
B
|
|
For the pair of similar figures in blue and green, use the given areas to find x.
Choices:
A:1
B:2
C:8
D:16
|
C
|
|
There is a right triangle with the length of hypotenuse as 5 and other sides as x and 3 \sqrt { 2 }. Find x.
Choices:
A:\sqrt { 7 }
B:3 \sqrt { 2 }
C:3 \sqrt { 3 }
D:3 \sqrt { 6 }
|
A
|
|
In the figure, a regular polygon is inscribed in a circle with center R. R S is perpendicular to K L. Find the measure of a central angle.
Choices:
A:30
B:60
C:90
D:120
|
B
|
|
In triangle X Y Z, Z W and W Y are equal. X W is perpendicular to Z Y. X Y and X Z are 18 + 2y and 5y - 6, respectively. Find X Z.
Choices:
A:5
B:17
C:18
D:34
|
D
|
|
In regular hexagon U V W X Y Z, W Y is perpendicular to X U, and the side is 12 centimeters long. Find W Y.
Choices:
A:12
B:6 \sqrt { 6 }
C:12 \sqrt { 3 }
D:36
|
C
|
|
Find the area of the rectangle, whose sides are 9 and 16 inches.
Choices:
A:25
B:50
C:72
D:144
|
D
|
|
There is a right triangle with hypotenuse length 17. Find x.
Choices:
A:\frac { 17 } { 2 }
B:\frac { 17 } { 2 } \sqrt { 2 }
C:\frac { 17 } { 2 } \sqrt { 3 }
D:17
|
C
|
|
Let A B be the median of trapezoid R S T Q. R A equals A Q, and S B equals B T. R S = 54 and Q T = 86. Find A B.
Choices:
A:27
B:54
C:70
D:86
|
C
|
|
In the circle, two chords A C and B D intersect. Find m \angle 2 if m \widehat B C = 30 and m \widehat A D = 20.
Choices:
A:20
B:25
C:30
D:155
|
D
|
|
In \odot X, Z W and Y V are diameters. Find m \angle V X W.
Choices:
A:25
B:65
C:115
D:180
|
B
|
|
Two triangles W S R and T V R are similar. W S and V T are parallel. W S is 8, and V T is 10. Find W R.
Choices:
A:6
B:8
C:10
D:12
|
B
|
|
In isosceles triangle R S T, \angle S R T is 70 degrees. Find m \angle R S T.
Choices:
A:55
B:70
C:75
D:80
|
A
|
|
Polygon A B C D \sim polygon A E F G, m \angle A G F = 108, G F = 14, A D = 12, D G = 4.5, E F = 8, and A B = 26. Find m \angle A D C.
Choices:
A:14
B:72
C:108
D:120
|
C
|
|
In the figure, four rays intersect and form 16 angles, and two upright rays are parallel. m \angle 3 = 110 and m \angle 12 = 55. Find the measure of \angle 1.
Choices:
A:55
B:110
C:125
D:135
|
B
|
|
Two rays intersect and form four angles all as x degrees. Find x.
Choices:
A:60
B:80
C:90
D:120
|
C
|
|
In the right triangle Q P R, \angle Q R P is 33 degrees, and \angle P Q S is 51 degrees. Connect Q S. Find m \angle 1.
Choices:
A:39
B:84
C:108
D:129
|
C
|
|
In the triangle with height x, two acute angles are 45 and 30 degrees. One of a right-angle side is bisected by a line from the top vertex. Find x.
Choices:
A:4
B:4 \sqrt { 2 }
C:4 \sqrt { 3 }
D:8
|
B
|
|
In triangle A B C, R, S, T are midpoints of A C, A B, and C B. A T, B R, and C S intersect at M. M C = 7, R M = 4, and A T = 16. Find M B.
Choices:
A:6
B:8
C:10
D:12
|
B
|
|
Find the value of the variable y in the right trapezoid.
Choices:
A:10
B:20
C:30
D:70
|
A
|
|
In the right triangle, the hypotenuse is 20 and two sides are y and x. Find y.
Choices:
A:4
B:6
C:8
D:10
|
D
|
|
In a pentagon UVWYZ, angle W is x + 8 degrees. Find m \angle W.
Choices:
A:38
B:38
C:76
D:152
|
C
|
|
A plane travels from Des Moines to Phoenix with a distance 110x + 53, on to Atlanta with a distance 150x + 91, and back to Des Moines with a distance 73.8x, as shown below. Find the distance in miles from Phoenix to Atlanta if the total trip was 3482 miles.
Choices:
A:53
B:73.8
C:110
D:1591
|
D
|
|
In the figure, m \angle 1 = 58, m \angle 2 = 47, and m \angle 3 = 26. EC and AB are parallel. Connect B E. Find the measure of \angle 5.
Choices:
A:43
B:47
C:58
D:73
|
B
|
|
The diagonals of rhombus F G H J intersect at K. If G H = x + 9 and J H = 5 x - 2, find x.
Choices:
A:2.75
B:3
C:5.5
D:9
|
A
|
|
The diameter of the circle is 6.2 cm. Find the circumference of the figure. Round to the nearest tenth.
Choices:
A:18.6
B:19.5
C:37.7
D:39.0
|
B
|
|
D is an external point to the circle, and A, C, F, E, B are on the circle. If m \widehat F E = 118, m \widehat A B = 108, m \angle E G B = 52, and m \angle E F B = 30, find m \widehat C F.
Choices:
A:30
B:44
C:108
D:118
|
B
|
|
In the right triangle with hypotenuse length 74 and two sides length 24 and x, use a Pythagorean Triple to find x.
Choices:
A:66
B:68
C:70
D:72
|
C
|
|
\angle B F C is 72 degrees, and B, C, D, A are on the circle. Find the measure of \angle C F D on \odot F with diameter A C.
Choices:
A:115
B:119
C:120
D:123
|
D
|
|
J K L M is a rectangle. M L P R is a rhombus. Connect M K and connect M P. \angle J M K \cong \angle R M P, m \angle J M K = 55, and m \angle M R P = 70. Find m \angle K L P.
Choices:
A:20
B:110
C:140
D:160
|
D
|
|
In a triangle with three sides length 29, 50, and 61. Find x. Round the angle measure to the nearest degree.
Choices:
A:98
B:103
C:108
D:113
|
A
|
|
In triangle A B C, A D, B E, and C F intersect at point Q. Q is the centroid and B E = 9. Find B Q.
Choices:
A:3
B:6
C:9
D:12
|
B
|
|
A B is a diameter, A C = 8 inches, and B C = 15 inches. Find the radius of the circle.
Choices:
A:7.5
B:8
C:8.5
D:17
|
C
|
|
In the right triangle with hypotenuse length 12 and two sides length x and z, find y.
Choices:
A:\frac { \sqrt { 2 } } { 2 }
B:\sqrt { 2 }
C:2 \sqrt { 2 }
D:4 \sqrt { 2 }
|
D
|
|
m is the perpendicular bisector of X Z, W Z = 14.9. Find W X.
Choices:
A:7.45
B:14.9
C:22.4
D:25.3
|
B
|
|
Lines l, m, and n are perpendicular bisectors of \triangle P Q R and meet at T. If T Q = 2 x, P T = 3 y - 1, T Q = 2 x, and T R = 8, find z.
Choices:
A:3
B:4
C:5
D:6
|
A
|
|
Two triangles A B E and A C D are similar with a shared vertex A. B E and C D are parallel. If A B = 12, A C = 16, and E D = 5, find A E.
Choices:
A:10
B:12
C:15
D:16
|
C
|
|
In \odot C, \angle R C M is x - 1 degrees, \angle R C L is 3 x + 5 degrees, and \angle M C N is 60 degrees. Find m \angle N C L.
Choices:
A:60
B:120
C:240
D:360
|
B
|
|
In a right triangle G E F, the hypotenuse G F is 16 and H F is 12. E H is the altitude of triangle G E F. Find the measure of the altitude drawn to the hypotenuse.
Choices:
A:2 \sqrt { 3 }
B:2 \sqrt { 6 }
C:4 \sqrt { 3 }
D:4 \sqrt { 6 }
|
C
|
|
In triangle A B C, AB = AC. \angle C A B and \angle A B C are both 2 x degrees. A B and B C are 3 and 4 y - 5 inches, respectively. Find x.
Choices:
A:20
B:30
C:40
D:50
|
B
|
|
In rhombus L M P Q, diagonal P L and Q M intersect at R. m \angle Q L M = 2 x^ { 2 } - 10, m \angle Q P M = 8 x, and M P = 10. Find the perimeter of L M P Q.
Choices:
A:10
B:40
C:70
D:140
|
B
|
|
The top and bottom sides of the quadrilateral are 22 and 37 ft. It's altitude is 23 ft. Find the area of the trapezoid.
Choices:
A:506
B:667
C:678.5
D:851
|
C
|
|
Triangle L M N is equilateral, and M P bisects L N. L M is 3 x + 1 and M N is 4 x - 2. Find the measure of the side of \triangle L M N.
Choices:
A:9
B:10
C:11
D:12
|
B
|
|
Parallelogram M N P Q with m \angle M = 10 x and m \angle N = 20 x, \angle M = \angle P and \angle N = \angle Q. Find \angle M.
Choices:
A:30
B:45
C:60
D:120
|
C
|
|
Three lines l, m, and p intersect at two points and form eights angles. Line l and m are parallel. If m \angle 5 = 7 x - 5 and m \angle 4 = 2 x + 23, find x.
Choices:
A:5.6
B:18
C:20
D:22
|
B
|
|
In parallelogram M N P R, diagonals M P and R N intersect at Q. M N = 3 x - 4, N P = 2 y + 5, R P = 20, and M R = 17.9. Find m \angle R M N.
Choices:
A:33
B:38
C:71
D:109
|
D
|
|
Point A, B, and C are on the circle. The radius angle of A C is 122 degrees. Find m \angle B.
Choices:
A:29
B:58
C:61
D:122
|
C
|
|
If \triangle L M N \sim \triangle Q R S, Q R = 35, R S = 37, S Q = 12, and N L = 5, find the perimeter of \triangle L M N.
Choices:
A:35
B:42
C:63
D:84
|
A
|
|
The two polygons are similar. R V = x m, R T = 18 m, A E = 3 m, C D = 5m, and B C = 4m. Find U T.
Choices:
A:12
B:20.5
C:22.5
D:35
|
C
|
|
Several triangles are combined together with 6 annotated angles. Find m \angle 6.
Choices:
A:25
B:28
C:35
D:55
|
C
|
|
\odot P \cong \odot Q. Chord R S is on \odot P with length 3x and chord T U is on \odot Q with length 7 x - 44. Find x.
Choices:
A:7
B:11
C:22
D:44
|
B
|
|
There is a right triangle with hypotenuse length x. One of the acute is 45 degrees and one of the side is 4. Find x.
Choices:
A:4 \sqrt { 2 }
B:4 \sqrt { 3 }
C:8
D:4 \sqrt { 5 }
|
A
|
|
Two triangles M Q N and M P O are similar with a shared vertex M. Q N and P O are parallel. M Q = 5, M N = 6, and Q P = x. Find Q P.
Choices:
A:2
B:3.6
C:5
D:6
|
B
|
|
There is a right triangle with hypotenuse length 42. The two sides are x and 38. Find x.
Choices:
A:8 \sqrt { 2 }
B:8 \sqrt { 3 }
C:8 \sqrt { 5 }
D:8 \sqrt { 7 }
|
C
|
|
In rhombus A B C D, diagonals A C and B D intersect at point E. A B = 2 x + 3 and B C = 5 x. Find m \angle A E B.
Choices:
A:45
B:60
C:90
D:180
|
C
|
|
Circle O has a radius of 13 inches, such as O C and O B. Radius O B is perpendicular to chord C D which is 24 inches long. If m \widehat C D = 134, find m \widehat C B.
Choices:
A:24
B:33
C:67
D:134
|
C
|
|
Circles G, J, and K all intersect at L. F H is the diameter of \odot G and G H is the radius. If G H = 10, find F H.
Choices:
A:5
B:10
C:20
D:25
|
C
|
|
Two triangles W in green and W' in blue are similar according to a reference point F. Find the scale factor from W to W'.
Choices:
A:\frac { 1 } { 3 }
B:\frac { 2 } { 3 }
C:\frac { 3 } { 4 }
D:\frac { 3 } { 2 }
|
A
|
|
In quadrilateral R Q T S, \angle R = \angle T = x degrees. Find m \angle R.
Choices:
A:58
B:60
C:122
D:124
|
A
|
|
There are two annotated angles of 5y and 60 degrees, and two annotated length x + 4 and 3 x - 6. Find x so that the quadrilateral is a parallelogram.
Choices:
A:3
B:5
C:12
D:18
|
B
|
|
In the right trangle A B C, \angle C = 90 degrees. A C = 24, A B = 26, and B C = 10. Express the ratio of \cos B as a decimal to the nearest hundredth.
Choices:
A:0.38
B:0.42
C:0.92
D:2.40
|
A
|
|
A B \cong D F. C E is perpendicular to A B and D F. C B = 9 x and D E = 2 x + 14. Find x.
Choices:
A:1
B:2
C:3
D:4
|
B
|
|
In \odot M, M K and M P are radii and perpendicular to chords F G and H J, respectively. F L = 24, H J = 48, and m \widehat H P = 65. Find F G.
Choices:
A:24
B:32
C:48
D:65
|
C
|
|
There are five lines shown. Three lines are parallel and the other two lines intersect with them. The spacing of the parallel lines is equal. Find x.
Choices:
A:0.5
B:1
C:1.5
D:2
|
B
|
|
In the right triangle, the hypotenuse is x length with an altitule of 8 length. The other two sides are y and z length. Find z.
Choices:
A:10
B:\frac { 32 } { 3 }
C:\frac { 40 } { 3 }
D:\frac { 50 } { 3 }
|
C
|
|
In H, the diameter is 18, L M = 12, and m \widehat L M = 84. J K is hypotenuse to L M at P. Find H P. Round to the nearest hundredth.
Choices:
A:2.29
B:3.35
C:5.65
D:6.71
|
D
|
|
There is a triangle with two acute angles of 27 and 52 degrees, along with an external angle as \angle 1. Find m \angle 1.
Choices:
A:21
B:27
C:52
D:79
|
D
|
|
There is a right triangle A B F on top of a rectangle C D E F. \angle C F D is labeled as \angle 2. Find m \angle 2.
Choices:
A:39
B:42
C:48
D:51
|
A
|
|
In \triangle P Q R, S T \parallel R Q. Triangle P S T is similar to triangle P R Q with a shared vertex P. If P S = 12.5, S R = 5, and P T = 15, find T Q.
Choices:
A:5
B:6
C:6.5
D:12.5
|
B
|
|
In the right triangle, an acute angle is labeled as \angle 4 with an external angle of 123 degrees. Find m \angle 4.
Choices:
A:33
B:43
C:57
D:123
|
A
|
|
A triangle with an acute angle of 30 degrees is within a circle, which forms the shaded region. Find the area of the shaded region.
Choices:
A:35.2
B:43.2
C:53.5
D:56.9
|
D
|
|
In the right triangle, an acute angle is 70 degrees and the hypotenuse is x length. Find x to the nearest hundredth.
Choices:
A:5.13
B:5.46
C:15.96
D:43.86
|
D
|
|
There is a rhombus in blue. Find the area of the rhombus.
Choices:
A:38
B:84
C:168
D:336
|
C
|
|
In parallelogram J K L M, diagonals J L and K M intersect at point R, and ML is 45, KL is 21. Find m \angle K J L if J K = 2 b + 3 and J M = 3 a.
Choices:
A:30
B:70
C:80
D:100
|
A
|
|
In triangle T Q S, TQ = 2, S Q = 5, and T S = 3. Find x if \triangle J L M \sim \triangle Q S T.
Choices:
A:1.5
B:2
C:3
D:4
|
A
|
|
There is an equilateral triangle with two sides 2 x + 11 and 6 x - 9. Find x.
Choices:
A:2
B:5
C:6
D:9
|
B
|
|
In the figure, there are four lines intersect at four points. Two pairs of lines are parallel to each other. m \angle 1 = 123. Find the measure of \angle 14.
Choices:
A:47
B:57
C:67
D:123
|
B
|
|
The diameters of \odot J and \odot K are on the same line with points A, B, C, and D. Circle J has a radius of 10 units, \odot K has a radius of 8 units, and B C = 5.4 units. Find J K.
Choices:
A:12.6
B:14.6
C:20.6
D:30.6
|
A
|
|
In the right isosceles triangle, the hypotenuse is 20. Find x. Round to the nearest tenth.
Choices:
A:1.4
B:7.1
C:14.1
D:15.6
|
C
|
|
In the right triangle, the two sides are y and 12 with an altitude of x. Find x.
Choices:
A:5
B:2 \sqrt { 11 }
C:10
D:4 \sqrt { 11 }
|
B
|
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