Download Test 1 Review

Math 135
Exam Review
Example 1
Find the value of x and the value of each angle.
5x+15
2
3x+55
4
3 x + 5 = 5 x + 15
3 x − 5 x + 55 = 3 x − 5 x + 15
− 2 x + 55 = 15
− 2 x + 55 − 55 = 15 − 55
− 2 x = −40
− 2 x − 40
=
−2
−2
x = 20
m∠3 = m∠6 = (20) + 15 = 115°
m∠1 = m∠2 = m∠4 = m∠5 = 65°
5
6
3
1
Polygons:
Example 2
Given that the sum of the interior angles of a polygon is 2880° , find the number of sides of the
polynomial.
2880 = (n − 2 )180
2880 (n − 2 )180
=
180
180
16 = n − 2
n = 16 + 2
n = 18
Example 3
Find the measure of the interior angle of a regular polygon with 15 sides.
I=
(n − 2)180 = (15 − 2)180 = 13 ⋅ 180 = 2340 = 156°
n
15
15
15
Example 4
Find the sum of the measures of the interior angles of a 15 sided polygon.
S = (n − 2)180 = (15 − 2)180 = 13 ⋅ 180 = 2340°
Example 5
Complete the following Chart
Regular
Polygon
Hexagon
Sum of the interior angles.
S = (6 − 2)180 = 4 ⋅ 180 = 720°
Octagon
S = (8 − 2)180 = 6 ⋅ 180 = 1080°
Measure of
interior angle.
720
I=
= 120°
6
I=
1080
= 135°
8
Measure of
Exterior Angle
360
I=
= 60°
6
I=
360
= 45°
8
Trigonometry
Example 6
Solve the following triangle.
B
c
18
125°
A
15
C
c 2 = a 2 + b 2 − 2ab cos C
c 2 = 18 2 + 15 2 − 2 ⋅ 18 ⋅ 15 ⋅ cos(125°)
c 2 = 324 + 225 − 540(− .574 )
c 2 = 549 + 310
c 2 = 859
c = 29.3
29.3
15
=
sin (125) sin A
29.3
15
=
.891 sin A
29.3 sin A = (.819)(15)
29.3 sin A = 12.3
sin A = .419 ⇒ ∠A = 24.7°
a = 18, b = 15, c = 29.3
∠A = 24.7, ∠B = 30.3°, ∠C = 125°
Example 7
Solve the following right triangle.
B
c
12
36°
A
b
12
b
tan 36° =
.726 =
12
b
12
⋅b
b
.726b = 12
.726 ⋅ b =
b = 16.5
sin 36° =
12
c
12
c
12
.588c = c
c
.588c = 12
.588 =
c = 20.4
a = 12, b = 16.5, c = 20.4
m∠A = 36°, ∠B = 54°, m∠C = 90°
C
Example 9
t
2
1
3
5
7
6
l
4
m
8
Given: ∠1 ≅ ∠8
Prove: l || m
Statement
Reason
1) ∠1 ≅ ∠8
Given
2) ∠1 ≅ ∠4
If two lines intersect the vertical angles formed
are congruent
3) ∠4 ≅ ∠8
Substitution
4) l || m
If two lines are cut by a transversal so the
corresponding angles are congruent, then the
lines are parallel.