Find each numbered angle



For problems 1-3, find each numbered angle and give a reason for each answer.

1.

2.

3.

4. Name the transformation shown in the figure below:

5. Given ΔABC with points A(1, 5),

B(6, 3) and C(8, 7). The triangle is

reflected across the y-axis to form

ΔA′B′C′. Find the point B′.

6. Given ΔABC with points A(-1, 5),

B(-2, -3) and C(2, 3). The triangle is

translated to form ΔA′B′C′ where A′

is the point (4, 2). Find the point B′.

7. Given ΔXYZ with points X(-3, 1),

Y(1, 4) and Z(5, 2). The triangle is

reflected across the x-axis to form

ΔX′Y′Z′. Find the point Z′.

8. Given ΔXYZ with points X(0, 2),

Y(0, 5) and Z(-2, 4). The triangle is

rotated 90° counterclockwise around the

origin to form ΔX′Y′Z′. Find the

point Z′.

9. Given ΔXYZ with points X(4, 0), Y(8, 0) and Z(5, 3). The triangle is rotated 180° counterclockwise around the origin to form ΔX′Y′Z′. Find the point Z′.

10. Can the following set of three sides

form a triangle? Yes or no.

a. 14, 20, 34

b. 4, 19, 4

c. 11, 5, 8

11. Find the maximum and minimum

values for the third side of a triangle

with two sides given

a. 60 and 62

b. 14 and 20

12. List the three angles of the triangle

in order from smallest to largest.

13. Find x and y in the figure given

M and N are midpoints.

14. Find x and y in the figure given

M and N are midpoints.

15. Find x in the rectangle

16. Find x in the rhombus.

17. Find x and y in the parallelogram.

For problems 18-31, if the two triangles shown are congruent, give a reason (SSS, SAS, ASA, AAS, or HL) why they are congruent and write a correct congruence statement. If there is not enough information to say the triangles are congruent, write “not congruent”.

18.

19.

20.

21.

22.

23.

24.

25.

26.

.27.

28.

29.

30.

31.

32. Find the sum of the measures of the

exterior angles of a 20-gon.

33. Find the measure of one exterior angle

of a regular 15-gon

34. The measure of one interior angle of a

regular polygon is 120°. Find the

number of sides of the polygon.

35. The measure of one exterior angle of a

regular polygon is 40°. Find the

number of sides of the polygon.

36. Find x in the diagram below:

37. Find the sum of the measures of the

interior angles of a hexagon.

38. Find the measure of one interior angle

of a regular 15-gon

39. The sum of the measures of the interior

angles of a polygon is 3240. Find the

number of sides of the polygon.

40. Find x in each diagram below.

a.

b.

For problems 41-53, find x in each figure.

41.

42.

43.

44.

45.

48.

49.

50.

51.

52.

53.

For problems 54-, find x in each figure.

54.

55. ∠1 and ∠2 are complementary.

m∠1 = 3x + 10

m∠2 = 2x

Find x.

56.

57. m∠ AOC = 130°

58. ∠1 and ∠2 are supplementary

m∠1 = 3x

m∠2 = x + 20

Find x.

59. Write the inverse, converse, and

contrapositive of the conditional

statement. Decide whether the

converse is true or false. If false,

provide a counterexample.

a. If x = 12, then x2 = 144.

b. If a number is odd, then it is divisible by three.

c. If a figure is a square, then all of its angles are right angles.

60. Write an indirect proof to show that a

triangle can have at most one obtuse

angle.

61. For each pair of points, find the

midpoint and length of the segment

connecting the points.

a. (-3, 1) and (4, 4)

b. (-1, 2) and (-7, -6)

For problems 62-63, use the Pythagorean Theorem to find the length of x.

62. 9

63.

For problems 64-68, find the area of each figure.

64.

65.

66.

67.

For problems 68-69, find the area and perimeter of each figure.

68.

69.

70. Find the area of the shaded region.

-----------------------

35°

4

3

2

1

55°

14

2x + 8

40°

y

65°

M

N

Z

1

4

35°

3

85°

2

24

x

N

M

y

78°

31°

21

10

18

Y

Z

X

2

55°

40°

1

45°

3

4

80

50

x

I

J

H

K

D

X

Y

W

V

B

A

D

C

J

M

K

L

W

X

Y

Z

N

O

A

B

X

Y

V

Z

W

B

A

D

C

E

H

F

G

D

G

F

E

E

H

F

G

W

X

Y

Z

P

T

Q

R

A

B

C

D

60

x

E

y

20

7

25

x

20

x

60

40

70

x

30

100

x

130

120

100

x

80

33

20

x

B

A

O

x + 5

75

9x

x + 30

x + 50

4x + 40

25

5x

25

x

x + 20

5x - 2

3x + 22

4x

2x + 10

70

55

x + 15

3x - 10

4x

50

50

100

x + 40

5x + 20

2x + 50

4x - 30

45

4x - 10

2x - 5

C

12

x

7

16

x

5

8

14

15

8

17

12

6

9

20

22

4

7

4

35

29

8

15

12

8

9

6

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