Download Polygon Review with Solutions

Acc. Geometery
Polygon Review
Name
Per/Sec.
Determine whether each of the following statements is always,
1 . A regular polygon is convex.
Date
, or never true.
2. Two sides of a polygon are
noncollinear.
sometimes
3.
An equilateral polygon is regular.
4.
A pentagon has a right angle.
5.
A trapezoid is a quadrilateral.
6.
A trapezoids has a right angle.
7.
The opposite angles of an isosceles
trapezoid are supplementary.
8.
A regular quadrilateral is a square.
9.
The sum of the measures of the
exterior angles of a convex polygon
is 3 60 .
1 0. An equiangular polygon is a regular
polygon.
1 1 . An equiangular triangle is a regular
triangle.
1 2. As the number of sides of a convex
polygon increases, the sum of the
interior angles increases.
1 3 . In an equiangular polygon with more
than 4 sides, an interior angle is
greater than an exterior angle.
1 4. In a convex polygon with more than
4 sides, an interior angle is greater
than an exterior angle.
1 5 . The measures of three of the angles
of a quadrilateral equal 1 20 , 75 ,
and 80 . Find the degree measure of
the fourth angle.
a) 80
b) 85
c) 90
d) 1 00
e) 1 05
1 6. Classify the given polygon.
a) quadrilateral
c) heptagon
e) decagon
b) pentagon
d) octagon
Page 2
1 7 . How many sides does an octagon
have?
a) 4
b) 5
c) 6
d) 8
e) 1 0
1 9. The sum of the measures of a
polygon is 1 440 . What kind of
polygon is it?
1 8. A regular hexagon has
of symmetry.
a) 2
b) 3
c) 4
lines
d) 5
e) 6
2 0. If " XYZ is a right isosceles triangle,
find the measure of the three angles
of the triangle.
a) hexagon
b) heptagon
a) 3 0 , 3 0 , 90
b) 3 0 , 60 , 90
c) octagon
d) decagon
c) 40 , 5 0 , 90
d) 45 , 45 , 90
e) dodecagon
e) 60 , 60 , 90
2 1 . Two angles of a triangle measure 1 8
and 7 7 . Find the measure of the
third angle.
a) 1 9
b) 3 6
c) 5 9
d) 64
e) 85
2 3 . In the given diagram, if m B = 1 1 2
and m A = 1 5 , find the degree
measure of the exterior BCD.
a) 5 3
b) 68
d) 1 65
e) 1 80
2 2 . In the given figure, m X = 47 and
m W = 92 , find m WYZ.
c) 1 2 7
a) 88
b) 1 00
d) 1 3 9
e) 1 5 6
c) 1 3 3
2 4. Which of the following is true about
the figure?
b=e
b) a + b = d + e
c) a + b = 2 ( d + e )
d) a + b 42 = d + e
e) a + b + d + e = 1 80
a)
Page 3
2 5 . Find the sum of the degree measures
of all the exterior angles of a
hexagon.
a) 3 6
b) 7 2
d) 1 80
e) 3 60
c) 90
2 6. Classify the given polygon.
a) pentagon
b) octagon
c) quadrilateral
d) hexagon
e) decagon
2 7 . Find the sum of the degree measures
of all the interior angles of a hexagon.
a) 5 40
b) 7 2 0
c) 1 080
d) 1 2 40
e) 1 400
2 8. Name the regular polygon with
interior angles which each
measure 1 2 0 .
a) triangle
b) pentagon
c) hexagon
d) octagon
e) decagon
2 9. Which of the following figures are
polygons?
I.
3 0. How many diagonals can be drawn
in a convex polygon with 1 1 sides?
a) 3 6
b) 3 9
c) 40
d) 44
e) 46
II.
III.
a) I only
b) III only
c) I and II only
d) I and III only
e) II and III only
3 1 . Which of the following polygons is a
quadrilateral?
a) square
b) pentagon
c) hexagon
d) triangle
e) octagon
3 2 . The sum of the measures of the
interior angles of a quadrilateral
is
degrees.
a) 2 7 0
b) 3 60
d) 7 2 0
e) 1 080
c) 5 40
Page 4
3 3 . The measures of three of the angles
of a quadrilateral equal 80 , 5 0 ,
and 90 . Find the degree measure of
the fourth angle.
a) 5 0
b) 80
d) 1 2 0
e) 1 40
3 4. What is the name of a polygon
having 4 sides?
c) 90
3 5 . What is the name of a polygon
having 1 0 sides?
3 6. What is the name of a polygon
having 1 2 sides?
3 7 . How many sides does a regular
polygon have if its perimeter is
65 cm and each side length is 1 3 cm?
3 8. In the diagram, polygon )*+,-./01
is regular and 0/ = 4. What is the
perimeter of this polygon?
3 9. What is the sum of the measures
of the interior angles of a convex
heptagon?
40. What is the measure of one interior
angle of a regular octagon?
41 . What convex polygon has an interior
angle sum of 7 2 0 ?
42 . Find the number of sides of a regular
polygon with an interior angle
measuring 60 degrees.
Page 5
43 . Find the number of sides of a regular
polygon with an interior angle
measuring 1 7 8 degrees.
44. Find the total number of diagonals
in a convex n-gon.
45 . The number of sides of a polygon is
increased by n, increasing the sum of
the measures of the interior angles
of the polygon by 7 2 0 . Find n.
46. In a convex polygon, the sum of
all the interior angles except one is
8000 . What is the least number of
sides this polygon can have?
47 . The sum of the measures of seven
angles of a convex decagon is 1 2 2 0 .
Of the remaining three angles,
precisely two are complementary
and precisely two are supplementary.
What is the measure of these three
angles?
48. Use the diagram to determine these
values:
a
49. An equiangular polygon has 1 8 sides.
What is the measure of one exterior
angle of this polygon?
b
c
d
e
f
g
h
5 0. A regular polygon has an exterior
angle of 1 5 . How many sides does
this polygon have?
Page 6
5 1 . What equiangular polygon has an
exterior angle measure of 1 1 . 2 5 ?
5 2 . A quadrilateral has 3 exterior angles
measuring 60 , 80 , and 7 0 . What
is the measure of the other exterior
angle?
5 3 . Solve for a.
5 4. In the diagram, points , and are midpoints of sides )* and )+,
respectively. If m + = 65 , what is
the measure of )-, ?
5 5 . In the diagram, m ) = x 6,
m * = x + 4, and m *+, = 1 2 0. What
is the measure of * ?
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