Geometry Chapter 6 Study Guide
1. Find sum of the interior angle of a 26-gon.
2. Find the number of sides of a regular polygon with an interior angle measure of 162 ̊
3. Find the measure of each exterior angle of a regular dodecagon.
4. Find the measure of each interior angle of a regular polygon with 20 sides.
5. Using
PATS fill in the blanks.
P
a. If SA = 88, then SL = ___________
A
L
b. If STP = 33o, then APT = ___________
S
c. If ST = 110 then AP = _______________
T
6. ABCD is a parallelogram. Find the value of each variable.
x=
57
A
B
y=
125 o
73
8a + 17
xo
D
5b + 12
yo
C
a=
b=
7. The length of one base of a trapezoid is 30 and the median is 22. Find the length of the other
base.
8. JKLM is an isosceles trapezoid.
24
J
K
48 ̊
M
Find the median, ∠M, and ∠J.
L
38
9. For the rhombus, find x and y
y
6x
35 ̊
10. The diagonals of square QRST intersect at point P. If 𝑄𝑃 = 2𝑥 + 8 and 𝑅𝑃 = 5𝑥 − 4, find QS.
11. In the parallelogram, find m∠1, m∠2 and m∠3
1
2
85 ̊
53 ̊
3
12. In the rectangle, find m∠1.
1
(4x+23)̊
(6x-5)̊
13. ABCD is a rectangle. 𝐴𝐶 = 𝑥 2 − 𝑥 and 𝐵𝐷 = 4𝑥 + 14 Find x and the length of each
diagonal.
14. State TRUE or FALSE for each statement:
A. Diagonals are congruent in a rectangle but not in a parallelogram. __________
B. All four sides are congruent in a rhombus but not a parallelogram. __________
C. Diagonals are perpendicular in a rhombus but not in a square. __________
D. Diagonals bisect both angles in a square but not in a rectangle. _________
15. A convex pentagon has interior angles with measures (2x 15)°, (6x 110)°, (5x 20)°, (4x 35)°,
and (3x
50)°. Find the measure of each interior angle.
16. Given the set of vertices, determine whether parallelogram ABCD is a rhombus, a rectangle, or a
square. Explain your reasoning. A(1, 5) B(6, 5) C(6, 10) D(1, 10)