NAME ________________________________________ DATE ___________________ PERIOD __________
6.1-6.6 Review: Polygons and Quadrilaterals
For each of the following regular polygons, find: a) the sum of the interior angles, b) the measure of
each interior angle, c) the sum of the exterior angles, and d) the measure of each exterior angle.
1. a) ___________
A triangle
b) ___________
c) ___________
d) ___________
2. a) ___________
A quadrilateral
b) ___________
c) ___________
d) ___________
3. a) ___________
A pentagon
b) ___________
c) ___________
d) ___________
4. a) ___________
A hexagon
b) ___________
c) ___________
d) ___________
5. a) ___________
b) ___________
c) ___________
d) ___________
A heptagon
6. a) ___________
An octagon
b) ___________
c) ___________
d) ___________
Find the value of ‘x” in each of the following.
7. _____________
8. a)___________
b) __________
9. a)__________
b) _________
For a 30-sided polygon, find:
a) the sum of the measures of the interior angles and
b) the sum of the measures of the exterior angles.
A 10- sided polygon, find:
a) the sum of the measures of the interior angles and
b) the sum of the measures of the exterior angles.
10. a)__________ For a 14-sided regular polygon, find:
a) the measure of each exterior angle, and
b) _________ b) the measure of each interior angle.
11. x = _________
If ABCD is a parallelogram, 𝑚∠𝐷 = 𝑋° and 𝑚∠𝐴 = (3𝑥 + 4)°, find
the value of 'x'. Hint: Draw a picture!
12.YA=_________ XYZW is a parallelogram with diagonals ̅̅̅̅
𝑋𝑍 and ̅̅̅̅̅
𝑌𝑊 that intersect
at point A. If YA = 2t and WA = 3t - 4, find YA.
13. x = _________
LMNO is a rectangle. If 𝑚∠𝐿𝑀𝑁 = (11𝑥 + 35)°, find the value of x.
14. x = _________
QRST is a rectangle. 𝑄𝑆 = 3𝑥 − 2 and 𝑅𝑇 = 48 − 2𝑥. Find the value of x.
15. x = _________
RWST is a rectangle. If 𝑅𝑍 = 2𝑥 + 5 and 𝑇𝑊 = 5𝑥 − 20. Find the value of x
16. ____________
DOGS is a rhombus. 𝑚∠1 = 37°. Find 𝑚∠4.
17. ____________
RATS is a rhombus. If 𝑚∠𝐴𝑇𝑆 = 96° and 𝑚∠𝐴𝑇𝑅 = 4𝑥°, find the value of 'x'.
18. ____________
BUGS is a rhombus. If 𝑚∠2 = 43°, find 𝑚∠3.
19. ____________
The diagram below shows a trapezoid with its midsegment. Find the value of 'x'.
20. ____________
The diagram below shows a trapezoid and its midsegment. Find the value of 'x'.
21. ____________
Find the value of 'x' in the trapezoid below.
22. ____________
In isosceles trapezoid LMNO below, LN = 3x + 3 and MO = 57.
Find the value of 'x'.
23.
The following figure is a parallelogram.
a = __________
x
b = __________
x = __________
y = __________
7
b
y
12
24. ____________
a
112
Let AC = 25 and DB = 5x. Find the value of 'x'.
B
A
D
C
25. ____________
MATH is an isosceles trapezoid with AT  MH. If mM = (3x – 9)°
and mH = (x + 3)°, find the value of ‘x’.
26. ____________
The measures of the bases of a trapezoid are 18 cm and 24 cm. What is the
measure of the trapezoid’s midsegment?
27. 𝑚 𝐿𝐻𝐽 = ___________
28. 𝑚 𝑷𝐿𝐻 = ___________
29. 𝑚 𝑃𝐾𝐿 = ___________
30. r = _________
Find the value of r in polygon JKLM.
31. x = ________
Find the value of x.
32. y = ________
Find y, and then find x.
33. x = ________
In kite HJKL, mKLP = 72°,
and mHJP = 49.5°.