Free Printable Angles & Rotations & Cross Sections

1.

What is the value of x?

a)

x = 160

b)

x = 40

c)

x = 80

d)

x = 360

2.

What is the measure of arc AYB

a)

50

b)

100

c)

180

d)

260

3.

Find a and b.

a)

a=74 degrees b=93 degrees

b)

a=93 degrees b=74 degrees

c)

a=87 degrees b=106 degrees

d)

a=106 degrees b=87 degrees

4.

Find the measure of the ?

a)

75˚

b)

190˚

c)

95˚

d)

150˚

5.

What is x?

a)

15

b)

23

c)

2

d)

92

6.

Find the measure of the indicated angle.

a)

60°

b)

120°

c)

30°

d)

90°

7.

Find the measure of the indicated angle.

a)

65°

b)

130°

c)

50°

d)

90°

8.

Solve for "?"

a)

70

b)

220

c)

110

d)

55

9.

How would you set up to find the measure of angles A and C?

a)

2x - 7 - x + 4 = 2x + 3

b)

2x-7 = x + 4

c)

2x - 7 + x + 4=180

10.

A circle has a radius of 8 cm. The measure of the arc of the shaded section is 72⁰. Which is closest to the area of the shaded section of the circle?

a)

10.1 cm²

b)

40.2 cm²

c)

50.3 cm²

d)

160.8 cm²

11.

The figure shows a right circular cone on top of a hemisphere with the same radius. To the nearest whole number, what is the volume of this solid?

a)

201 cm³

b)

256 cm³

c)

278 cm³

d)

309 cm³

12.

In the diagram, a tangent and a line drawn to the point of tangency form a right triangle. Solve for "?" (the length of the hypotenuse)

a)

15

b)

6

c)

-24

d)

14

13.

Find the value of X

a)

8.5

b)

3.6

c)

7.2

d)

9.2

14.

Is line AB tangent to the circle?

Note: the segment labeled 12 is a radius and so is the segment from the center to point A

a)

YES

b)

NO

c)

Can't Tell

15.

Find the area of the shaded sector of circle O. The radius is 6 inches and the central angle is 100°. Express answer to the nearest tenth of a square inch.

a)

25.2 in²

b)

28.5 in²

c)

31.4 in²

d)

38.2 in²

16.

What is the area of the shaded SECTOR? Round to the nearest hundredth.

a)

9.42 u²

b)

113.10 u²

c)

284.3 u²

d)

452.39 u²

17.

Given the following inscribed quadrilateral, what is the value of y?

a)

10

b)

20

c)

30

d)

40

18.

Given the following inscribed quadrilateral, what are the values of x and y?

a)

x = 70; y = 120

b)

x = 30; y = 20

c)

x = 20; y = 30

d)

x = 70; y = 40

19.

What is the measure of angle A?

a)

34°

b)

180°

c)

112°

d)

79°

20.

Find the value of x

a)

100

b)

105

c)

95

d)

90

21.

Quadrilateral ABCD is inscribed in the circle. Which sentence is true?

a)

A and B are supplementary

b)

A and C are supplementary

c)

m∠ A = m∠ B

d)

m∠ C = m∠ D

22.

Solve for x.

a)

14

b)

10

c)

11

d)

2

23.

Solve for x.

a)

14

b)

10

c)

11

d)

2

24.

Solve for Y.

a)

103

b)

95

c)

93

d)

105

25.

Assume that all the lines that appear tangent are tangent. Find the perimeter

a)

54

b)

36

c)

48

d)

42

26.

Find the perimeter of the polygon.

a)

77.8

b)

73.4

c)

78.8

d)

67.4

27.

If AB=8, AE=19, and CE=17, what is the measure of segment BC?

a)

6 units

b)

8 units

c)

8.5 units

d)

11 units

28.

Assume that the lines that appear to be tangent are tangent. O is the center of the circle. Find the value of x to the nearest tenth.

a)

11.7

b)

10.8

c)

13.0

d)

14.2

29.

Find the perimeter of the triangle.

a)

A

b)

B

c)

C

d)

D

30.

Find the length of BC.

a)

2

b)

3

c)

9

d)

14

31.

What is the value of x?

a)

22

b)

25

c)

15

d)

20

32.

Assume that lines that appear to be tangent are tangent. O is the circle. What is the value of x?

a)

90

b)

140

c)

220

d)

360

33.

Assume that lines that appear to be tangent are tangent. O is the center of the circle. What is the value of x?

a)

90

b)

309

c)

129

d)

39

34.

Assume that lines that appear to be tangent are tangent. O is the center of the circle. What is the value of x?

a)

160

b)

20

c)

70

d)

90

35.

The polygon circumscribes a circle. What is the perimeter of the polygon?

a)

140

b)

45

c)

70

d)

190

36.

A point B is 17cm away from the centre O of a circle. AB is the tangent to the circle at A. Given that AB = 15 cm, find the radius of the circle.

a)

8 cm

b)

9 cm

c)

2 cm

d)

16 cm

37.

Find the value of X

a)

3

b)

16

c)

8

d)

12

38.

What is the measure of ∠PTQ?

a)

100°

b)

140°

c)

180°

d)

120°

39.

Value of x is equal to 90°

a)

True

b)

False

40.

Using lines tangent to the circle, find the value of x.

a)

57

b)

137

c)

47

d)

257

41.

Determine y.

a)

30

b)

60

c)

90

d)

180

42.

How big is angle b?

a)

50 degrees

b)

60 degrees

c)

70 degrees

d)

75 degrees

43.

Solve for x.

a)

5

b)

20

c)

40

d)

85

44.

What shape will the horizontal cross-section of a sphere be?

a)

Dome

b)

Circle

c)

Ellipse

d)

Rectangle

45.

Describe the cross section.

a)

circle

b)

oval

c)

semi-circle

d)

trapezoid

46.

Which 3-D solid is created when the rectangle is rotated about the horizontal line?

a)

b)

c)

d)

47.

What is the area of the cross-section if the diameter of the base is 6 feet and the height of the cylinder is 8 feet.

a)

24 ft²

b)

48 ft²

c)

8 ft²

d)

4 ft²

48.

What is the area of the cross-section if the diameter of the base is 6 feet and the height of the cylinder is 8 feet.

a)

24 ft²

b)

48 ft²

c)

8 ft²

d)

4 ft²

49.

What is the area of the cross-section if the diameter of the base is 6 feet and the height of the cylinder is 8 feet.

a)

24 ft²

b)

48 ft²

c)

8 ft²

d)

4 ft²

50.

What is the area of the cross-section if the diameter of the base is 6 feet and the height of the cylinder is 8 feet.

a)

24 ft²

b)

48 ft²

c)

8 ft²

d)

4 ft²

51.

The right triangle as shows is rotated $360\degree$ about the $y-axis$ in three dimensions. What is the 3-Dimensional solid resulting from the rotation?

a)

cone

b)

cylinder

c)

pyramid

d)

prism

52.

Name the solid that would be formed by rotating the shape about a given axis.

a)

Sphere

b)

Cone

c)

Cyliner

d)

Frustum

53.

What is the cross section depicted here?

a)

Square

b)

Triangle

c)

Pyramid

d)

plane

54.

Which of the following shows a TRAPEZOID cross-section?

a)

b)

c)

d)

55.

Identify the solid of revolution generated by revolving the region around the fixed line 𝓁.

a)

b)

c)

d)

56.

Identify the solid of revolution generated by revolving the region around the fixed line 𝓁.

a)

b)

c)

d)

57.

What is the cross section of the 3D figure?

a)

Rectangle

b)

Trapezoid

c)

Triangle

d)

Square

58.

What is the cross section of the shape?

a)

Triangle

b)

Rectangle

c)

Square

d)

Trapezoid

59.

What is the cross section of the solid?

a)

Square

b)

Rectangle

c)

Circle

d)

Cylinder

60.

What is the cross section of the figure?

a)

Rectangle

b)

Circle

c)

Cylinder

d)

Triangle

61.

Find the cross section of the 3d shape.

a)

Cylinder

b)

Cone

c)

Circle

d)

Square

62.

Which 2-D shape could be revolved about the vertical line to create the 3-D solid?

a)

b)

c)

d)

63.

Which 3 dimensional object would result from rotating the figure around the axis drawn?

a)

Rectangle

b)

Rectangular prism

c)

Cylinder

d)

Rectangular pyramid

64.

what figure was rotated about the y axis to produce this cylinder?

a)

cylinder

b)

rectangle

c)

square

d)

triangle

65.

Identify the solid of revolution generated by revolving the region around the fixed line 𝓁.

a)

b)

c)

d)

66.

What shape does this cross section make? (parallel to base)

a)

Rectangle

b)

Circle

c)

Triangle

d)

Square

67.

a)

15

b)

20

c)

14/3

d)

3/14

68.

Solve for x.

a)

x = 21

b)

x = 22

c)

x = 4

d)

x = 42

69.

Given the picture Find the r value. Then find the $Tan\theta,\ Cot\theta\ function\ values.$

Select the correct answer.

a)

$r=2\sqrt{5},Tan\theta=-2,Cot\theta=-\frac{1}{2}$

b)

$r=4\sqrt{5\ },\ \tan\theta=-\frac{1}{2},\ \cot\theta=-2$

c)

$r=\sqrt{20},Tan\theta=\frac{1}{2},Cot\theta=2$

d)

$r=2\sqrt{5},\ Tan\theta=-\frac{1}{2},Cot\theta=-2$

70.

What shape will the vertical cross-section of a cube be?

a)

Square

b)

Triangle

c)

Trapezoid

d)

Circle

71.

Describe the cross section.

a)

trapezoid

b)

triangle

c)

rectangle

d)

square

72.

What shape will the angled cross-section of a rectangular pyramid be?

a)

Triangle

b)

Rectangle

c)

Trapezoid

d)

Square

73.

What is the value of x?

a)

17

b)

34

c)

68

d)

Impossible to determine from the information given.

74.

What is the value of x?

a)

1

b)

2

c)

4

d)

Impossible to determine from the information given.

75.

What is the value of x?

a)

25.5

b)

43

c)

78

d)

Impossible to determine from the information given.

76.

What is the value of x?

a)

3

b)

6

c)

9

d)

Impossible to determine from the information given.

77.

Find the missing length.

a)

x = 12

b)

x = 11

c)

x = 15

d)

x = 9

78.

Solve for x.

a)

14

b)

20

c)

8

d)

10

79.

Solve for x.

a)

36

b)

20

c)

52

d)

12

80.

Solve for x.

a)

17

b)

29

c)

20

d)

19

81.

Solve for x.

a)

11

b)

27

c)

29

d)

10

82.

Solve for x.

a)

9

b)

23

c)

10

d)

12

83.

Solve for x.

a)

8

b)

21

c)

10

d)

12

84.

Solve for x.

a)

20

b)

-2

c)

3

d)

8

85.

Find $m\angle V$

a)

100

b)

80

c)

180

d)

360

86.

Find $m\angle X$

a)

100

b)

80

c)

180

d)

360

87.

Find $m\angle W$

a)

180

b)

360

c)

75

d)

105

88.

Find $m\angle V$

a)

180

b)

360

c)

75

d)

105

89.

Find DE

a)

14

b)

7

c)

28

d)

2

90.

Find x

a)

0

b)

9

c)

-1.5

d)

2

91.

Find the length of AB

a)

6

b)

11

c)

17

d)

68

92.

What is the value of x?

a)

10

b)

No Solution

c)

5

d)

2

93.

What is the value of y?

a)

3

b)

No Solution

c)

5

d)

2

94.

Segment DE is ____________.

a)

an angle bisector

b)

a perpendicular segment

c)

a median

d)

a midsegment

95.

Find the missing length.

a)

12

b)

48

c)

24

d)

18

96.

What is the value of x?

a)

x = 15

b)

x = 13

c)

x = 12

d)

x = 11

97.

Find the measure of DG.

a)

14

b)

28

c)

12

d)

16

98.

Find the missing angle of the trapezoid.

a)

65

b)

115

c)

180

d)

None of these

99.

Find the value of x.

a)

7

b)

8

c)

85

d)

None of these

100.

Find the measure of ∠1:

a)

79°

b)

101°

c)

72°

d)

180°

101.

Which of the following statements is false?

a)

all four angles are congruent

b)

the legs are congruent

c)

the diagonals are congruent

d)

the base angles are congruent

102.

Find the measure of n:

a)

117

b)

63

c)

25

d)

39

103.

Find the missing angle of the trapezoid.

a)

65

b)

115

c)

180

d)

None of these

104.

If this Trapezoid is isosceles, what is measure of angle 1?

a)

105 degrees

b)

75 degrees

105.

The figure is a parallelogram.
Solve for x.

a)

1

b)

11

c)

7

d)

6

106.

The figure is a parallelogram.
Solve for x.

a)

7

b)

1

c)

5

d)

2

107.

The figure is a parallelogram.
Solve for x.

a)

7

b)

2

c)

0

d)

4

108.

The figure is a parallelogram.
Solve for x.

a)

1

b)

10

c)

4

d)

5

109.

Solve for X

a)

22

b)

16

c)

40

d)

35

110.

solve for X

a)

24

b)

90

c)

14

d)

100

111.

solve for Y

a)

20

b)

15

c)

60

d)

12

112.

solve for X

a)

19

b)

20

c)

33

d)

53

113.

solve for Y

a)

20

b)

15

c)

60

d)

12

114.

Solve for Y

a)

25

b)

17

c)

8

d)

12

115.

Find m∠PRQ.

a)

39°

b)

90°

c)

51°

d)

15°

116.

Solve for x.

a)

5

b)

20

c)

40

d)

85

117.

Angle R is right because

a)

the triangles is circumscribed and SQ is a radius

b)

the triangles is inscribed and SQ is a radius

c)

the triangles is inscribed and SQ is a diameter

d)

triangle QRS is inscribed

118.

In the inscribed quadrilateral ABCQ, opposite angles are

a)

congruent

b)

supplementary

c)

complementary

d)

sum to 360^o

119.

Given the following inscribed quadrilateral, what is the value of y?

a)

10

b)

20

c)

30

d)

40

120.

Find the measure of

\angle E.

(a)

121.

Find the measure of

\angle U.

(a)

122.

What is the measure of

$arc\ GI$

(a)

123.

The rectangle shown has coordinates (3, 2), (-2, 2), (-2, -1), (3, -1)

What is the length of the longest side of the rectangle?

(a)

124.

You design a tree house using a coordinate plane. You plot the vertices of the floor at J (2, 1), K (2, 8), L(9, 8), and M (9, 1). The coordinates are measured in feet. What is the area of the tree house?

a)

28 feet²

b)

49 feet²

c)

56 feet²

d)

64 feet²

125.

What is the perimeter of a rectangle with corners at (2,2), (2,-4), (-5,-4), and (-5,2).

a)

13 units

b)

26 units

c)

42 units

d)

10 units

126.

What is the perimeter of a rectangle with corners at (2,2), (2,-4), (-5,-4), and (-5,2).

a)

13 units

b)

26 units

c)

42 units

d)

10 units

127.

What is the area of the triangle?

a)

2.5 square units

b)

3 square units

c)

3.5 square units

d)

4 square units

128.

What is the area of the figure?

a)

11 square units

b)

15 square units

c)

25 square units

d)

30 square units

129.

What is the area of the triangle?

a)

60 square units

b)

90 square units

c)

45 square units

d)

30 square units

130.

What is the perimeter (in units) of the triangle formed by the points (-3,1), (-3,5), and (4,1)?

a)

65

b)

8.06

c)

14

d)

19.06

131.

What is the area (in square units) of the triangle formed by the points (-3,1), (-3,5), and (4,1)?

a)

19.06

b)

14

c)

28

d)

8.06

132.

Square ABCD has vertices A(-2,-3), B(4, -1), C(2, 5), and D(-4, -3)and . What is the area of the square?

a)

$2\sqrt{10}$

b)

$4\sqrt{10}$

c)

40

d)

20

133.

The vertices of square RSTV have coordinates R(-1,5), S(-3,1), T(-7,3) and V-5,7). What is the perimeter of RSTV?

a)

$\sqrt{20}$

b)

$\sqrt{40}$

c)

$4\sqrt{20}$

d)

$4\sqrt{40}$

134.

What is the perimeter of the rectangle? (Round to the nearest tenth)

a)

18

b)

about 23.6

c)

about 25.1

d)

about 21.6

135.

What is the perimeter of the triangle? (Round to the nearest tenth)

a)

12

b)

about 13.2

c)

21

d)

about 12.6

136.

The measure of an inscribed angle that intercepts a semicircle is a(n) ___________ angle.

a)

right

b)

acute

c)

obtuse

137.

What angle corresponds to $\angle4$ ?

a)

$\angle4$

b)

$\angle5$

c)

$\angle3$

d)

$\angle2$

Angles & Rotations & Cross Sections

Total questions: 137

Worksheet time: 7hrs 38mins

Similar Resources on Wayground