Name: 
 

Angles and Polygons



Multiple Choice
Identify the choice that best completes the statement or answers the question.
 

 1. 

Judging by appearance, classify the figure in as many ways as possible.
mc001-1.jpg
a.
rectangle, square, quadrilateral, parallelogram, rhombus
b.
rectangle, square, parallelogram
c.
rhombus, trapezoid, quadrilateral, square
d.
square, rectangle, quadrilateral
 

 2. 

Find the values of the variables and the lengths of the sides of this kite.
mc002-1.jpg
a.
x = 9, y = 13; 7, 15
c.
x = 9, y = 13; 11, 20
b.
x =13, y = 9; 7, 15
d.
x =13, y = 9; 11, 11
 

 3. 

What is the most precise name for quadrilateral ABCD with vertices A(–5, 2), B(–3, 6), C(6, 6), and D(4, 2)?
a.
quadrilateral
b.
rectangle
c.
parallelogram
d.
rhombus
 

 4. 

Which statement is true?
a.
All quadrilaterals are rectangles.
b.
All quadrilaterals are squares.
c.
All rectangles are quadrilaterals.
d.
All quadrilaterals are parallelograms.
 

 5. 

Judging by appearances, which figure is a trapezoid?
a.
mc005-1.jpg
c.
mc005-3.jpg
b.
mc005-2.jpg
d.
mc005-4.jpg
 

 6. 

ABCD is a parallelogram. If mc006-1.jpg then mc006-2.jpg The diagram is not to scale.
mc006-3.jpg
a.
66
b.
124
c.
114
d.
132
 

 7. 

LMNO is a parallelogram. If NM = x + 15 and OL = 3x + 5 find the value of x and then find NM and OL.
mc007-1.jpg
a.
x = 7, NM = 20, OL = 22
c.
x = 7, NM = 22, OL = 22
b.
x = 5, NM = 20, OL = 20
d.
x = 5, NM = 22, OL = 20
 

 8. 

For the parallelogram, if mc008-1.jpg and mc008-2.jpg find mc008-3.jpg The diagram is not to scale.
mc008-4.jpg
a.
mc008-5.jpg=9
b.
mc008-6.jpg=17
c.
mc008-7.jpg=173
d.
mc008-8.jpg=163
 

 9. 

Find the values of the variables in the parallelogram. The diagram is not to scale.
mc009-1.jpg
a.
mc009-2.jpg mc009-3.jpg mc009-4.jpg
c.
mc009-8.jpg mc009-9.jpg mc009-10.jpg
b.
mc009-5.jpg mc009-6.jpg mc009-7.jpg
d.
mc009-11.jpg mc009-12.jpg mc009-13.jpg
 

 10. 

In parallelogram DEFG, DH = x + 3, HF = 3y, GH = 4x – 5, and HE = 2y + 3. Find the values of x and y. The diagram is not to scale.
mc010-1.jpg
a.
x = 6, y = 3
b.
x = 2, y = 3
c.
x = 3, y = 2
d.
x = 3, y = 6
 

 11. 

Find AM in the parallelogram if PN =9 and AO = 4. The diagram is not to scale.
mc011-1.jpg
a.
8
b.
4
c.
9
d.
4.5
 

 12. 

Find values of x and y for which ABCD must be a parallelogram. The diagram is not to
scale.
mc012-1.jpg
a.
x = 10, y = 38
b.
x = 10, y = 21
c.
x = 10, y = 7
d.
x = 7, y = 10
 

 13. 

In the rhombus, mc013-1.jpg Find the value of each variable. The diagram is not to scale.
mc013-2.jpg
a.
x = 12, y = 84, z = 20
c.
x = 6, y = 84, z = 10
b.
x = 6, y = 174, z = 20
d.
x = 12, y = 174, z = 10
 

 14. 

Find the values of a and b.The diagram is not to scale.
mc014-1.jpg
a.
mc014-2.jpg mc014-3.jpg
c.
mc014-6.jpg mc014-7.jpg
b.
mc014-4.jpg mc014-5.jpg
d.
mc014-8.jpg mc014-9.jpg
 

 15. 

Find mc015-1.jpg in the kite. The diagram is not to scale.
mc015-2.jpg
a.
m∠1=51,  m∠3=51
b.
m∠1=39,  m∠3=39 
c.
m∠1=39,  m∠3=51
d.
m∠1=51,  m∠3=39
 

 16. 

Find the values of x and y. The diagram is not to scale.
mc016-1.jpg
a.
x = 77, y = 59
c.
x = 57, y = 77
b.
x = 77, y = 57
d.
x = 41, y = 57
 

 17. 

Which figure is a convex polygon?
a.
mc017-1.jpg
c.
mc017-3.jpg
b.
mc017-2.jpg
d.
mc017-4.jpg
 

 18. 

The chips used in the board game MathFuries have the shape of hexagons. How many sides does each MathFuries chip have?
a.
5
b.
6
c.
8
d.
10
 

 19. 

How many sides does a regular polygon have if each exterior angle measures 20?
a.
17 sides
b.
20 sides
c.
21 sides
d.
18 sides
 

 20. 

Find the missing angle measures. The diagram is not to scale.
mc020-1.jpg
a.
x = 124, y = 125
c.
x = 114, y = 56
b.
x = 56, y = 114
d.
x = 56, y = 124
 

 21. 

The jewelry box has the shape of a regular pentagon. It is packaged in a rectangular box as shown here. The box uses two pairs of congruent right triangles made of foam to fill its four corners. Find x.
mc021-1.jpg
a.
18°
b.
54°
c.
36°
d.
72°
 

 22. 

The sum of the measures of two exterior angles of a triangle is 255. What is the measure of the third exterior angle?
a.
75
b.
115
c.
105
d.
95
 

 23. 

The Polygon Angle-Sum Theorem states: The sum of the measures of the interior angles of an n-gon is ____.
a.
mc023-1.jpg
b.
mc023-2.jpg
c.
mc023-3.jpg
d.
mc023-4.jpg
 

 24. 

Complete this statement. The sum of the measures of the exterior angles of an n-gon, one at each vertex, is ____.
a.
(n – 2)180
b.
360
c.
mc024-1.jpg
d.
180n
 

 25. 

Complete this statement. A polygon whose sides all have the same length is said to be ____.
a.
regular
b.
equilateral
c.
equiangular
d.
convex
 

 26. 

Find mc026-1.jpg. The diagram is not to scale.
mc026-2.jpg
a.
107
b.
117
c.
63
d.
73
 

 27. 

Write an equation in slope-intercept form of the line through point J(–5, 6) with slope –4.
a.
y = -4x + 26
c.
y = -4x + 14
b.
y = 4x +14
d.
y = -4x - 14
 

 28. 

Write an equation for the horizontal line that contains point E(–3, –1).
a.
x = –1
b.
x = –3
c.
y = –1
d.
y = –3
 

Short Answer
 

 29. 

Find the measures of an interior angle and an exterior angle of a regular polygon with 6 sides.
 

 30. 

What type of quadrilateral has exactly one pair of parallel sides?
 

 31. 

Complete this statement: For parallelogram ABCD, sa031-1.jpg
Then state a definition or theorem that justifies your answer.
sa031-2.jpg
 

Essay
 

 32. 

Explain how you can determine, without measuring any angles, whether a quadrilateral is a rectangle.
 

Other
 

 33. 

Is the quadrilateral a parallelogram? Explain. The diagram is not to scale.
ot033-1.jpg
 

 34. 

Two consecutive angles of a quadrilateral are right angles, but the quadrilateral is not a rectangle. Can the quadrilateral be a parallelogram? Explain.
 

 35. 

Can this quadrilateral be a parallelogram? Explain.
ot035-1.jpg
 



 
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