Parallel Lines and Transversals
PG 106 in you book has a section called "Example 4, Identifying Interior and Alternate Exterior Angles" Use the graphic on this page to answer the following:
If the angle labeled 1 has a measurement of 85, what is the measurement of angle 2?
95
Why? Because they are two angles along the same side, so angle 1 plus angle 2 have to equal 180. We can find angle 2, by taking 180 and subtracting angle 1. 180 - 85 = 95
A triangle has angles measuring x, 35, and 35. Find the value of x.
110
Why? The interior angles of a triangle add up to 180 degrees, so we solve the following problem:
x+35+35=180
so, x+70=180
Thus, x=110
Check the figure shown for number 22 on page 115. Ignore the question, but use the image for this question.
If angle y is 40 degrees, and angle x is 90 degrees, what is the measurement of angle z?
130 degrees
Why? The exterior angle of a triangle equals the sum of two nonadjacent interior angles
What is the formula to find the sum of the interior angles of a polygon?
Use this to prove why the interior angles of a triangle always add up to 180.
S= (n-2) 180
Where n = the number of sides of a polygon.
A triangle has 3 sides, so:
S = (3-2) 180
S = (1) 180
S = 180
What is the sum of the exterior angles of any polygon?
360 degrees
PG 106 in you book has a section called "Example 4, Identifying Interior and Alternate Exterior Angles" Use the graphic on this page to answer the following:
If angle 4 is 92 degrees, what is the measurement of angle 5?
92 degrees
Why? Angle 5 is an alternate interior angle to angle 4, which are, by definition congruent.
A Triangle has interior angles of 32, 63, and x. What is the measurement of x?
85
why? 32+63+x=180
Check the figure shown for number 22 on page 115. Ignore the question, but use the image for this question.
If angle y is 88 degrees, and angle x is 47 degrees, what is the measurement of angle z?
135
Why? The exterior angle of a triangle equals the sum of two nonadjacent interior angles
Find the sum of the interior angles of an octagon.
1080
Why? Octagons have 8 sides.
S = (8-2) 180
S = (6) 180
S = 1080
A triangle has external angles of 30, 110, and x. Find x
why?
30 + 110 + x =360
140 + x = 360
x = 220
PG 106 in you book has a section called "Example 4, Identifying Interior and Alternate Exterior Angles" Use the graphic on this page to answer the following:
If angle 8 is 87 degrees, what is the measurement of angle 3?
93 degrees
Why? Angle 8 would be congruent to angle 4, because they in the same position on their respective parallel line. Because angle 4 is 87 degrees, angle 3 must be 180 - 87, which is 93.
A Triangle has interior angles of 102, x, and x. Find the measurement of x
39
Why? 102 + x + x = 180
so, 102 + 2x = 180
2x = 78
x = 39
Check the figure shown for number 22 on page 115. Ignore the question, but use the image for this question.
If angle y is 35 degrees, and angle x is 2b degrees and angle z is 3b, what is the measure of angle z?
105
Why?
35 + 2b = 3b
35 = b
if angle z is 3b, then 3 times 35 = 105
Find the sum of the interior angles of a heptagon.
900
Why? A heptagon has 7 sides.
S = (7-2) 180
S = (5) 180
S = 900
A 4-sided figure has exterior angles of 50, 127, 91, and x. Find x
92
Why?
x +50 + 127 +91 =360
x +268 =360
x = 92
PG 106 in you book has a section called "Example 4, Identifying Interior and Alternate Exterior Angles" Use the graphic on this page to answer the following:
If the angle labeled 6 is 76 degrees, what are the measures of all other angles from 1 to 8?
Angles 6, 7, 2, and 3 measure 76 degrees.
Angles 8, 5, 4, and 1 measure 104 degrees.
Why? Angles 6 and 7 are opposites, and thus will always measure the same. Angles 2 and 3 are in the same positions on the other parallel line. Angle 8 shares a line with angle 6, so they must add up to 180 degrees, so angle 8 has to be 104. 5 is opposite 8, making them congruent. 1 and 4 share the same position on the other parallel line.
A triangle has interior angles of 90, (x+28) and x. Find x
31
Why?
90 + (x + 28) + x = 180
118 + 2x = 180
2x = 62
x = 31
Check the figure shown for number 22 on page 115. Ignore the question, but use the image for this question.
If angle y is 30 degrees, and angle x is h degrees and angle z is (2h-12), what is the measure of angle z?
72
Why?
30 +h = (2h - 12)
so 42=h
angle z is (2h-12)
2(42)-12 =72
A heptagon has interior angles of 121, 160, 112, x, 130, 128, 125. Find the Value of x.
124
Why?
S = (7-2) 180
S = 900
121 + 160 + 112 + x + 130 + 128 + 125 = 900
so, x = 124
A triangle has exterior angles of 124, z, and (z + 26). find z.
105
Why?
124 + z + (z + 26) =360
2z +150 = 360
2z = 210
z = 105
PG 106 in you book has a section called "Example 4, Identifying Interior and Alternate Exterior Angles" Use the graphic on this page to answer the following:
Identify two sets of alternate interior angles and two sets of alternate exterior angles
(Check page 105 for a definition of interior and exterior angles)
Alternate Interior Angles:
2 and 7
4 and 5
Alternate exterior Angles:
3 and 6
1 and 8
Why? Check out the "Key Idea" on page 106 to help understand the concept better.
A Triangle has interior angles of 105.6, x, and 28.4. Find x and classify the triangle as obtuse, acute or right.
46, obtuse
Why?
105.6 + 28.4 + x = 180
134 + x = 180
x = 46
The largest angle is bigger than 90 degrees, making the triangle obtuse.
Check the figure shown for number 22 on page 115. Ignore the question, but use the image for this question.
If angle y is 54 degrees, and angle x is (b + 7) degrees and angle z is (2b - 15) degrees, what is the measure of b? how about angle x? angle z? angle w?
b = 76
x = 83
z = 137
w = 43
Why? Solve for b.
54 + (b+7) = 2b-15
b=76
Solve for angle x:
b+7 = 76+7 = 83
Solve for angle z:
2b-15 = 2 (76) - 15 = 137
Solve for w:
180-137=43
A Pentagon has interior angles measuring 2x, 145, 145, 2X, and 110. Find the value of x, and the value of the missing angles.
x=35. the missing angles =70
Why?
S = (5-2) 180
S = (3) 180 = 540
2x + 145 + 145 + 2x + 110 = 540
4x = 140
x = 35
But each missing angle equals 2x, so 2(35) =70
In pottery class, you are making a pot that is shaped as a regular hexagon. What is the measure of each exterior angle of the regular hexagon?
60
Why?
By definition, a regular polygon is one where all sides are equal. This means the measures of the exterior angles will also be the same.
x + x + x + x + x + x = 360
6x = 360
x = 60