Download Find the number of sides of a regular polygon if the measure of each

Geometry
Chapter 8 Review
Name ______________________
Solve and be sure to show HOW you got your answer.
Find the sum of the measures of the interior angles of a polygon having:
1. 9 sides
2. 13 sides
Find the sum of the measures of the exterior angles of a polygon having:
3. 14 sides
4. 109 sides
Find the measure of the remaining interior angle of each of the following figures.
5. hexagon with angles: 95, 154, 80, 145, 76
6. pentagon with angles of 116, 138, 94, 88
Find the measure of each interior angle of a regular polygon having:
7. 30 sides
8. 90 sides
Find the measure of each exterior angle of a regular polygon having:
9. 24 sides
10. 45 sides
Can the given angle represent the measure of an exterior angle of a regular polygon?
Explain why.
11. 46
12. 15
13. 27
14. 72
Find the number of sides of a regular polygon if the measure of each interior angle is:
15. 162
16. 140
17. 168
Find the number of sides of a regular polygon if the measure of each exterior angle is:
18. 90
19. 45
20. 36
The diagonals of rhombus STUV intersect at W. Given that m  UVT = 31.8, TU = 20, and
TW = 17, find the indicated measures.
21. m  UVS
22. m  TWU
23. m  TUV
24. UW
25. SU
26. VT
S
V
T
U
Find the value of the unknown(s). Show work to justify your answers!!!
(some pictures NOT drawn to scale)
27.
28.
136
85
150
(3x + 40)
(5x – 10)
x
50
60
(6x + 20)
(4x + 15)
4x
x = ______
29.
5x
x = ______
regular hexagon
30. Find the number of sides of a regular n-gon
if the measure of an exterior angle is 18
y
x
Find n (number of sides) = ______
x = ______ y = ______
31.
120
165
160

156

k = _________
153

k
176
2
135
171
32. The polygon in the center is a regular pentagon.
The triangles on each side of the pentagon are
isosceles.
148
x
x = _________
2y + 10
33.
34. ABCD is a square.
DF = 2x - 3
AC = 3x + 7
100
40
8x
A
B
1
F
2
(3b + 5)
5x + 15
D
x = ______
m1 ______
m2 = ______
length of AD = ______
perimeter of ABCD = _____
x = ______
y = ______
b = ______
35. The figure is a rhombus
36. ABCD is a rhombus.
A
4y  8
D
14
R
A
O
60
20
O
76
1
K
C
B
x = ______
mODC = ______
mABC = ______
mDCB = ______
P
24
T
m1 = ______
y = ______
(radical answers)
37. TRAP is an isosceles trapezoid
mRTP = 78
5x  15
126
C
mTRA = ______
mRAP = ______
mAPT = ______
OK = ______
If RP = 46, AT = 3b + 7 then b = ____
38.
T
b9
PSTU is a rectangle, MP  RS ,
YZ is the midsegment of isosceles trapezoid MRTU.
COAT is a kite.
42
C 75
x
d = _______
M
P
b = _______
A
d + 13
y
z
S
12
V
x = _______
Y
30
R
X
W
Z
y = _______
z = _______
T
U
O
39.
MR = 3x  10
UT = 2x + 3
YZ = 9
x = ______
40.
PM = 2y
UT = 6y + 1
MR = 5
y = ______
YZ = ______
Fill in the blank with always, sometimes or never.
41. A rectangle is ___________________a parallelogram.
42. A parallelogram is ____________________a rhombus
43. A rhombus is __________________ a square
44. A quadrilateral is ____________________a trapezoid.
45. An isosceles trapezoid is ___________________a parallelogram.
46. A rectangle is _____________________ a square.
List all the quadrilaterals for which the given property is true. Use the key:
I (Isosceles trapezoid), K (Kite), P (Parallogram), S (Square), R (Rectangle), RH (Rhombus), T(Trapezoid)
47. the diagonals are congruent
48. diagonals are perpendicular
49. all sides are congruent
50. all angles are congruent
51. diagonals bisect each other
52. opposite sides are congruent
53. diagonals bisect opposite angles
54. diagonals are congruent AND perpendicular
55. consecutive angles are supplementary
56. exactly one pair of sides is parallel
For each quadrilateral named, three vertices are given. Graph these vertices and then find the location of the 4th
vertex. Write its coordinates. Use your knowledge of special quadrilaterals and coordinate geometry.
57. MATH is an isosceles trapezoid.
M (-2, 4)
A (1, 2)
T (1, -1)
H ________
59. MATH is a rectangle.
M (-3, 0)
A (-2, 2)
T (2, 0)
H ________
58. MATH is a kite.
M (1, -1)
A (-1, 3)
T (1, 5)
H ________
60. MATH is a parallelogram.
M (-1, 1)
A (4, 2)
T (2, -1)
H ________
Find the area of each figure. Round answers to the nearest tenth.
61)____________
62)_______________
7cm.
12cm.
13cm.
9cm.
8cm.
63)_____________
12cm.
15cm.
9cm.
8cm.
64) The exterior angles of a triangle are in the measure of 2x  5 , 4x and x . Find the measure of
each exterior angle.
Tell whether each statement is always, sometimes, or never true.
65) As the number of sides of a polygon increases, the sum of the interior angles increases.
_____________________
66) If the number of sides of an equiangular polygon is doubled, the measure of each exterior angle is
halved. _____________________
67) The measure of an exterior angle of a regular decagon is greater than the measure of an exterior
angle of a regular pentagon. _____________________
68) As the number of sides of a polygon increases, the sum of the exterior angles decreases.
_____________________
D
F
C
69) Write a two-column proof.
Given: ABC  CDA
Prove: ABCF is a trapezoid.
A
B