Download Unit 3 Review Packet 2 1. Find the sum of the measures of the

Unit 3 Review Packet 2
1. Find the sum of the measures of the angles of the figure.
2. ABCD is a parallelogram. If
A
then
B
D
C
3. ABCD is a parallelogram. If
A
then
The diagram is not to scale.
B
D
____
The diagram is not to scale.
C
4. WXYZ is a parallelogram. Name an angle congruent to
X
Y
N
W
A.
Z
B.
C.
D.
5. Find AM in the parallelogram if PN =12 and AO = 5. The diagram is not to scale.
M
N
A
P
O
6. LMNO is a parallelogram. If NM = x + 34 and OL = 5x + 6, find the value of x and then find NM and OL.
O
N
L
M
7. If
find
A
D
so that quadrilateral ABCD is a parallelogram. The diagram is not to scale.
B
C
8. If
and
be a parallelogram. The diagram is not to scale.
O
N
L
____
M
9. Which statement is true?
A. All parallelograms are rectangles.
B. All quadrilaterals are parallelograms.
C. All rectangles are squares.
D. All parallelograms are quadrilaterals.
find the values of x and y for which LMNO must
10. In rectangle KLMN, KM =
and LN = 45.5. Find the value of x.
K
L
N
M
11. Find the values of a and b. The diagram is not to scale.
a°
111°
68°
b°
12.
and
Find
The diagram is not to scale.
R
|
|
S
||
||
U
T
13. Find the measures of an interior angle and an exterior angle of a regular polygon with 8 sides.
14. What type of quadrilateral has all sides congruent?
15. Isosceles trapezoid ABCD has legs
find the value of y.
and
and base
If AB = 4y – 5, BC = 2y – 5, and CD = 5y – 17,
16. B is the midpoint of
D is the midpoint of
and AE = 21. Find BD. The diagram is not to scale.
C
B
D
A
E
17. Identify parallel segments in the diagram.
C
8
6
B
D
8
6
A
5
F
5
E
18. Find the value of x. The diagram is not to scale.
72°
105°
x°
____ 19. Which description does NOT guarantee that a quadrilateral is a parallelogram?
A. a quadrilateral with consecutive angles supplementary
B. quadrilateral with two opposite sides parallel
C. a quadrilateral with the diagonals bisecting each other
D. a quadrilateral with both pairs of opposite sides congruent
20. Use less than, equal to, or greater than to complete this statement: The sum of the measures of the exterior
angles of a regular 5-gon, one at each vertex, is ____ the sum of the measures of the exterior angles of a regular 4-gon, one at each vertex.
What are
|
1
The diagram is not to scale.
|
21. In the rhombus,
|
|
3
2
22. Find the measure of the numbered angles in the rhombus. The diagram is not to scale.
33º
1
3
2
23. DEFG is a rectangle. DF = 6x – 2 and EG = x + 8. Find the value of x and the length of each diagonal.
24. What is the sum of the angle measures of a 24-gon?
25. In rectangle PQRS, PR = 20x – 20 and QS = x + 512. Find the value of x and the length of each diagonal.
P
Q
S
R
26. In quadrilateral ABCD,
and
A
D
B
C
. For what value of x is ABCD a rhombus?
27. In quadrilateral ABCD,
and
A
. For what value of x is ABCD a rectangle?
B
E
D
C
28. The sum of the angle measures of a polygon with s sides is 3600. Find s.
29. Find
in the kite. The diagram is not to scale.
|
1
3
2
B
||
||
D
29°
|
A
C
30. What is the measure of one angle in a regular 20-gon?
31. In parallelogram DEFG, DH = x + 2, HF = 2y, GH = 2x – 2, and HE = 2y + 2. Find the values of x and y. The
diagram is not to scale.
D
E
H
G
F
32. A road sign is in the shape of a regular decagon. What is the measure of each angle on the sign? Round to the
nearest tenth.
33. Find the missing values of the variables. The diagram is not to scale.
123°
127°
x°
y°
77°
34. Points B, D, and F are midpoints of the sides of
The diagram is not to scale.
EC = 30 and DF = 17. Find AC.
A
B
F
C
D
E
35. Find the value of x.
14
2x – 9
36. Find the value of x. The diagram is not to scale.
45
x
45
35
24
24
37. The sum of the measures of two exterior angles of a triangle is 257. What is the measure of the third exterior
angle?
38. Use the information in the diagram to determine the height of the tree. The diagram is not to scale.
150 ft
(
39. Use the information in the diagram to determine the measure of the angle x formed by the line from the point
on the ground to the top of the building and the side of the building. The diagram is not to scale.
X
(
52º
40. Find values of x and y for which ABCD must be a parallelogram. The diagram is not to
scale.
A
B
4x – 18
y + 13
4y – 5
x + 12
D
C
41. How many sides does a regular polygon have if each exterior angle measures 30?
42. Find the value of x. The diagram is not to scale.
110°
x°
57°
43. Find the measure of each interior and exterior angle. The diagram is not to scale.
5
4
115 o
6
1
2
9
8
7
3
44. Find the values of the variables. Show your work and explain your steps. The diagram is not to scale.
o
31
x
w
y
v
o
68
z
45. Find the values of x, y, and z. The diagram is not to scale.
46°
13°
58°
x°
z°
y°
46. This jewelry box has the shape of a regular pentagon. It is packaged in a rectangular box as shown here. The
box uses two pairs of congruent right triangles made of foam to fill its four corners. Find the measure of the
foam angle marked.
x
x
47. For the parallelogram, if
and
3
find
The diagram is not to scale.
4
2
1
48. Use less than, equal to, or greater than to complete this statement: The measure of each exterior angle of a
regular 7-gon is ____ the measure of each exterior angle of a regular 4-gon.
49. Find the value of x. The diagram is not to scale.
(3x + 10)º
148º
(x)º
112º
50. Find the length of the midsegment. The diagram is not to scale.
47
56
4x + 2
56
47
4x + 44
Find the value of each variable. The diagram is
|
|
51. In the rhombus,
not to scale.
3
1
|
|
2
52. Which description does NOT guarantee that a trapezoid is isosceles?
A. both pairs of base angles congruent
B. congruent legs
C. congruent bases
D. congruent diagonals
53. A nonregular hexagon has five exterior angle measures of 51, 60, 68, 53, and 57. What is the measure of the
interior angle adjacent to the sixth exterior angle?
54. B is the midpoint of
and D is the midpoint of
Solve for x, given
C
B
D
A
E
55. Find the values of the variables and the lengths of the sides of this kite.
y–2
|
x+ 2
||
||
|
2x + 3
x+ 6
56. Find the value of x. The diagram is not to scale.
Given:
,
,
S
R
T
U
and
57. Find the values of the variables in the parallelogram. The diagram is not to scale.
109
20
y°
x°
z°
58. For what values of x and y must this quadrilateral be a parallelogram? Find the lengths of the sides. The
diagram is not to scale.
7x
2x + 2
4y
8y + 11
59. In the parallelogram,
and
J
Find
The diagram is not to scale.
K
O
M
L
60. In the parallelogram,
and
P
Q
O
S
R
Find
The diagram is not to scale.
Unit 3 Review Packet 2
Answer Section
1.
2.
3.
4.
5.
6.
7.
900
119
100
C
5
x = 7, NM = 41, OL = 41
133
7
8. x = 10, y =
2
9. D
10. 3.5
11.
12. 20
13. m (interior) = 135
m (exterior) = 45
14. rhombus
15. 12
16. 10.5
17.
18. 33
19. B
20. equal to
21.
22.
23. x = 2, DF = 10, EG = 10
24. 3960
25. x = 28, PR = 540, QS = 540
26. 3
27. 14
28. 22
29.
30. 162
31. x = 6, y = 4
32. 144
33. x = 107, y = 53
34. 34
35. 8
36. 70
37. 103
38. 75 ft
39. 52
40. x = 10, y = 6
41. 12 sides
42. 13
43.
44.
[4]
[3]
[2]
[1]
45.
46.
47.
48.
49.
50.
51.
52.
53.
54.
55.
56.
57.
58.
59.
60.
Because the three interior angles of a triangle have measures with sum 180, w + 31 +
90 = 180, so w = 59. Because vertical angles are congruent, y = 59. Because supplementary angles have measures with sum 180, x = v = 121.
Because the three interior angles of a triangle have measures with sum 180, z + 68 +
y = z + 68 + 59 = 180, so z = 53.
small error leading to one incorrect answer
three correct answers, work shown
two correct answers, work shown
36°
158
less than
45
42
x = 45, y = 45, z = 9
C
109
x = 3, y = 7; 5, 9
76
x = 5, y = 3; 12, 35
107
94