Polygon Unit Test Review 2015 RTI

Directions: You must show all work for all problems below. For the problems where you have a quadrilateral and use their properties, justify the set up, and provide the geometry. (Some may not have the information to do everything i.e. if no points are there, you cannot show the geometry). Failure to do so will result in a zero. 

1.	 Find the sum of the measures of the interior angles of a convex 39-gon.

2.	 Find the sum of the measures of the exterior angles of a convex 21-gon.

3.	 Find the measure of an interior angle of a regular polygon with 20 sides. Round to the nearest tenth if necessary.

4.	 Find the measure of each exterior angle for a regular heptagon. Round to the nearest tenth if necessary.

5. A regular polygon has an exterior angle with a measure of 20o. Find the number of sides.

6. A regular polygon has an interior angle with a measure of 120o. Find the number of sides. 

7. Fill in the following table: 

Number of Sides	Name of Polygon	
3		
4		
5		
6		
7		
8		
9		
10		
11		
12		
n		

8. 	For parallelogram RSTU, find mÐRSU and mÐRUS.

mÐRSU = ____________				mÐRUS = ____________

9. Solve for the missing angle or variable for the following PARALLELOGRAMS. 

a.) Find x.					b) Find m<1. 				C. Find all variables. 

				
10. 	Find x so that the quadrilateral is a parallelogram. Then find the side length of MP, QP, and MN.

x = _________    MP = ____________   QP = ______________   MN = _______________	M			

11. 	ABCD is a square. If AC = 16 and BD = 2x + 4, find x.

12. Rhombus Practice: 
a.) For rhombus ABCD, mÐ8 = 35, find the mÐ1, mÐ2, mÐ3, mÐ4, mÐ5, mÐ6, and mÐ7.

					mÐ1 = _______	mÐ2 = _______

					mÐ3 = _______	mÐ4 = _______

					mÐ5 = _______	mÐ6 = _______

					mÐ7 = _______

b.) For rhombus GHJK, find mÐ1

13. ABCD is a rectangle. If mÐ1 = 20, find the mÐ2, mÐ3, mÐ4, mÐ5, and mÐ6.
	
mÐ2 = _______	mÐ3 = _______

mÐ4 = _______	mÐ5 = _______

mÐ6 = _______	

14. For isosceles trapezoid CDEF, find mÐF, mÐE, mÐD, and EF.
								
mÐF = ________	mÐD = ________

 				mÐE = ________	EF = _________

15. Find all of the missing angles.

v = __________ 		w = _________		x = __________	y = _________		z = __________

16. LK is the midsegment of trapezoid HJNM. Find MN if HJ = 5 and LK = 25.

17. For isosceles trapezoid GHJK, find <1. 

18. Given isosceles trapezoid ABCD, EF is the midsegment. Find EF, AD, and m<AEF if AB=10, CD = 20, AE = y + 5, FC = 2y – 10, and m<EFC =130

EF = _______

AD = ______

m<AEF = _______

19. For isosceles trapezoid MNOP, find m<M, m<O, m<QNO and mÐMNQ if <P = 65ᵒ.

20. Find all ? for the coordinates. ABCD is a square. 

A(0,b) 

B(?,?) 

D(?,?) 

C(?,?) 

21. Find all ? for the coordinates. ABCD is a rhombus. 

A(0,3b) 

B(3a,?) 

D(?,?) 

C(?,?) 

22.  Classify QRST with vertices Q(-5,7), R(-3, 4), S(3, 8), and T(1, 11). SHOW ALL WORK!!!! Show all distances, all slopes, find the area and perimeter of the figure. 

Q

	

R

23.  Classify ABCD SHOW ALL WORK!!!! Show all distances, all slopes, find the area and perimeter of the figure.