Download 6-2 Angles in Polygons

AP Honors Contemporary Topics of Math
Unit 6 – More Geometry
Name ___________________
Date ___________ Period ___
6–2
Angles in Polygons
Triangle Sum Theorem – The sum of the three interior angles of a triangle
is 180º
Find the value of x .
x
x
1.
2.
60°
3.
60°
40°
55°
x
4.
5.
x
x +10
75°
6.
65°
50°
x
x
50°
112°
x
Quadrilateral Sum Theorem – The sum of the four interior angles of any quadrilateral
is 360º
Find the value of x .
7.
75°
8.
60°
2x - 10
105°
9.
x
135°
2x +20
55°
x
x
Properties of Parallelograms – Opposite angles of parallelograms are congruent;
Consecutive angles of parallelograms are supplementary.
Find the value of x for each parallelogram.
2x
10.
11.
100°
12.
75°
x
5x - 24
2x +30
B
C
39º
Use the parallelogram at the right to find the indicated measures.
13. mC  __________
15. mADC  __________
14. mBDA  __________
A
16. mABD  __________
72º
Choices for #13 to #17:
a) 36º
b) 69º
d) 111º
e) 108º
ac) 42
ad) 53
17. mBDC  __________
D
c) 72º
ab) 39º
ae) 19
Sums of the Interior Angles of Regular Polygons –
Formula S  180(n  2) if n = number of sides.
18.
a)
b)
c)
d)
20.
Find the sum of the interior angles
of an octagon. (8 sides).
720°
900°
1080°
1260°
19.
a)
b)
c)
d)
Find the measure of the interior angle, x,
of the regular hexagon. (6 sides).
21.
Find the sum of the interior angles
of a pentagon. (5 sides).
540°
480°
520°
450°
Find the measure of the interior angle, x,
of a decagon. (10 sides).
x
a)
b)
c)
d)
80°
100°
120°
144°
a)
b)
c)
d)
80°
100°
120°
144°
22.
The measure of one interior angle of a
regular polygon is 150º. Using this
measurement, the polygon has how
many sides?
23.
Find the measure of one exterior angle of
a regular hexagon.
?
a)
b)
c)
d)
8
10
12
15
a)
b)
c)
d)
30°
45°
60°
20°
Find the equation of the line that contains the given two coordinates.
Write the equation in the form y = m x + b .
24. ( -4 , 15 ) and ( 2 , -9 )
a)
b)
c)
d)
y  0.25 x  16
y  0.25 x  14
y  4 x  31
y  4 x  1
Solve the system of equations.
2 x  y  7
x  3y  7
25.
a)
b)
c)
d)
(
(
(
(
-4 , 0 )
1 , -2 )
-3 , -1 )
-2 , 3 )