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Review for Polygon Test
NAME_____________________________________________
Find the sum of the measures of the interior angles of the following convex polygons.
1. quadrilateral
2. hexagon
3. decagon
4. pentagon
You are given the measure of each interior angle of a regular n-gon. Find the value of n.
5. 108 
6. 135 
7. 144 
Find the sum of the exterior angles of the convex polygon.
8. heptagon
9. nonagon
10. Find the measure of each interior and exterior angle of a regular convex octagon.
Fill in the blank with A for Always, S for Sometimes, or N for Never.
11.__________ The diagonals of a quadrilateral are congruent.
12.__________ The diagonals of a rectangle are congruent.
13.__________ The diagonals of a trapezoid are congruent.
14.__________ The diagonals of a square bisect each other.
15.__________ The four sides of a trapezoid are congruent.
16.__________ The diagonals of a rectangle bisect the angles of the rectangle.
17.__________ The diagonals of a rectangle are perpendicular to each other.
18.__________ The four angles of a trapezoid are congruent.
19.__________ The diagonals of a rhombus are perpendicular.
20.__________ A rhombus is a rectangle.
21.__________ A square is a rectangle.
22.__________ A rhombus is a square.
23.__________ Consecutive angles of a parallelogram are complements.
24.__________ The midsegment of a trapezoid is perpendicular to the base.
25.__________ Consecutive sides of a parallelogram are congruent.
26.__________ Trapezoids are parallelograms.
27.__________ Parallelograms are quadrilaterals.
28.__________ Isosceles trapezoids are parallelograms.
29.__________ All angles of a parallelogram are congruent.
30.__________ Opposite angles of an isosceles trapezoid are congruent.
31.
List the 6 ways to determine if a quadrilateral is a PARALLELOGRAM.
a.)
b.)
32.
Solve for x.
50 
(3x + 17) 
110 
c.)
(x – 4) 
d.)
e.)
f.)
95 
Write the definition, postulate, or theorem which would be used to prove the following quadrilaterals
are parallelograms. If there is not enough information, write “none”.
K
33. B
34. B
35. J
C
C
A
A
D
L
D
M
For each of the following, solve for the variables. SHOW ALL WORK!!
36.
Given: Rectangle BCDE;
EC = 9x – 35
BD = 4x + 70
x = _____
If BC = 24 and EA = 13 find
BE = ______
Perimeter of BCDE = ______
37.
F
G
E
C
B
I
H
FG = 3y + 2
HI = 5y – 6
GH = y + 4
A
FI = ______
D
E
38.
Given: FGHI
FE = 4x + 12
EH = 2x + 48
FH = ______
Given: Rhombus USTV
m VUT = 5x – 30
m SUT = 4x – 10
m STU = ______
39.
U
V
VU = 2x + 6
US = x + 9
ST = ______
Perimeter of USTV = _____
R
Given: Square NOPQ
NO = 7x + 11
N
OP = 3x + 83
x = ______
m  NMQ = ______
m  PNQ = ______
m  QNO = ______
S
Q
O
M
P
T
40.
Given: MNOP; MO = 6; LN = 4
LO = ______
ML = ______
MN = ______
m PLM = ______
41.
M
P
L
O
N
Given: Trap HOYA; HA  OY ;
m  HAY = 106 
SY = x + 1
H
O
HS = 2x – 9
AS = x
SO = x + 4
S
x = ______
m  AHO = ______
m  HOY = ______
A
Y
m  OYA = ______