Download Geometry Assignment #27 Interior Angles of a Polygon 1. Find the

Geometry
Assignment #27
Interior Angles of a Polygon
1.
Find the sum of the measures of the interior angles of:
a) a pentagon
b) an octagon
c) a polygon having 20 sides
2.
Find the measure of each angle of a:
a) regular pentagon
b) regular octagon
3.
Find the number of sides of a regular polygon if each interior angle is:
a) 90°
b) 120°
c) 140°
d) 160°
4.
Find the number of sides of a polygon if the sum of the interior angles is:
a) 180°
b) 360°
c) 540°
d) 1440°
5.
Find the value of x in the diagram to the right, if
ABC & DEFG , and HF = EF.
6.
7.
c) regular polygon having 20 sides
B
A
H
80
Two supplementary angles are in the ratio 4:11.
Find the measure of the smaller angle.
The angles of Δ XYZ are consecutive even integers.
What is the measure of the largest angle in Δ XYZ?
C
E
D
x
F
G
R1. Solve for the positive root of y 2 − 2y = 35 .
R2. Find the area of a triangle whose altitude measures 8 inches and whose base is 5½ inches
long.
R3. In ∆ABC, m∠A = 2x , m∠B = 90 , and m∠C = x . Find the measures of ∠A and ∠C .
R4. Find x.
R5. Find the length of a leg.
20
(3x - 50) °
(7x)°
45°
Island Trees Math Department
R6. Find the length of AC.
R7. Given equilateral triangle ABC. If BD is
7 3 , find the area of the triangle. (10th)
B
B
10
A
x
D
C
15
A
C
D
R8. Which statement is logically equivalent to “If a triangle is an isosceles triangle, then it has
two congruent sides”?
(1) If a triangle does not have two congruent sides, then it is an isosceles triangle.
(2) If a triangle does not have two congruent sides, then it is not an isosceles triangle.
(3) If a triangle is not an isosceles triangle, then it has two congruent sides.
(4) If a triangle is an isosceles triangle, then it does not have two congruent sides.
1.
a) 540
b) 1080
c) 3240
2.
a) 108
b) 135
c) 162
3.
a)
b)
c)
d)
4
6
9
18
4.
a)
b)
c)
d)
3
4
5
10
5.
6.
7.
160
48
62
R1.
R2.
R3.
R4.
R5.
R6.
R7.
R8.
7
22
A = 60, C = 30
23
10 2
20
84.9
2
Island Trees Math Department