Download Lesson 5.2 • Exterior Angles of a Polygon

Lesson 5.2 • Exterior Angles of a Polygon
Name
Period
Date
In Exercises 1–3, find each lettered angle measure.
1. a _____, b _____
116°
2. a _____, b _____
3. a _____, b _____,
c _____
a
a
2x
82°
b
c
3x
x
b
a 82°
134°
72°
b
4. How many sides does a regular polygon have if each exterior
angle measures 30°?
5. How many sides does a polygon have if the sum of the measures of the
interior angles is 3960°?
6. If the sum of the measures of the interior angles of a polygon equals
the sum of the measures of its exterior angles, how many sides does
it have?
7. If the sum of the measures of the interior angles of a polygon is twice
the sum of its exterior angles, how many sides does it have?
is the side of an equilateral triangle. XS
is the side of a
8. XT
is the side of a regular pentagon. XH
is the side
square. XP
of a regular hexagon. XO is the side of a regular octagon.
mTXS _____
mSXP _____
mPXH _____
mHXO _____
S
P
H
T
O
mOXY _____
9. If the number of sides of a regular polygon doubles,
X
Y
what happens to the measure of each exterior angle?
10. Find each lettered angle measure.
150°
c
d
a
95°
b
11. Construct an equiangular quadrilateral that is not regular.
12. Use a protractor and a ruler to draw a regular polygon.
32
CHAPTER 5
Discovering Geometry Practice Your Skills
©2003 Key Curriculum Press
7. (See flowchart proof at bottom of page.)
6. 170°; 36 sides
7. 15 sides
8. Given: Isosceles ABC
BC
and
with AC
median CD
bisects ACB
Show: CD
8. x 105°
9. x 105°
Flowchart Proof
C
10. x 18°
11. mHFD 147°
LESSON 5.2 • Exterior Angles of a Polygon
A
D
B
CD is a median
Given
AC BC
AD BD
CD CD
Given
Definition of
median
Same segment
ADC BDC
2
1. a 64°, b 1383°
2. a 102°, b 9°
3. a 156°, b 132°, c 108°
4. 12 sides
5. 24 sides
6. 4 sides
7. 6 sides
8. mTXS 30°, mSXP 18°, mPXH 12°,
mHXO 15°, mOXY 45°
9. Each exterior angle is cut in half.
SSS Conjecture
10. a 135°, b 40°, c 105°, d 135°
ACD BCD
11.
CPCTC
CD bisects
ACB
Definition of
bisect
12.
LESSON 5.1 • Polygon Sum Conjecture
1. a 103°, b 103°, c 97°, d 83°, e 154°
108°
108°
108°
2. x 121.7°, y 130°
3. p 172°, q 116°, r 137°, s 90°, t 135°
4. a 92°, b 44°, c 51°, d 85°, e 44°,
f 136°
5. mE 150°
3. x 64°, y 43°
70° D
A
LESSON 5.3 • Kite and Trapezoid Properties
2. x 124°, y 56°
110°
125°
85°
108°
1. x 30
C
B
108°
4. x 12°, y 49°
150°
E
Lesson 4.8, Exercise 7
CD CD
Same segment
CD is an altitude
Given
98
ADC and BDC
are right angles
Definition of altitude
ANSWERS
ADC BDC
ADC BDC
AD BD
CD is a median
Both are right angles
SAA Conjecture
CPCTC
Definition of
median
AC BC
A B
Given
Converse of IT
Discovering Geometry Practice Your Skills
©2003 Key Curriculum Press