Parallel and Transversals
A transversal cuts two horizontal parallel lines. The angle that is formed on the top left is 53 degrees. What angle is formed on the bottom left?
127
A triangle includes angles that measure 23, 65, and x. What is the measure of x?
92
What is the equation to solve for the SUM of the interior angles of a polygon? Define the variable.
(n-2) * 180
n is the number of sides.
Find the similar Triangles.
a. Triangle with angles 75, 55, x
b. Triangle with angles 75, 40, x
c. Triangle with angles of 50, 55, x
a and c
What is a regular polygon?
Any polygon where all interior angles are equal and all sides are the same.
Two lines cross one another. The bottom angle is 135. The top angle is (x+49). Solve for x. Then, tell the measurement of the angles on the right and left.
x= 135-49, so X=86
The angles to the left and right equal 45.
A triangle contains angles that measure 90, x+32, and x. Find the value of the two missing angles.
x = 29
x+32 = 61
A 5-sided polygon has EXTERIOR angles of x, x+45, x+17, x and x. What is the measure of each angle?
x+x+45+x+17+x+x=360
so
x=59.6
x+45 = 104.6
x + 17 = 76.6
Find the similar triangles:
a. Triangle with angles 90, 30, x
b. Triangle with angles 60, 30, x
b. Triangle with angles 90, 50, x
a and b are similar.
What is the difference between an interior and exterior angle?
Interior angles are INSIDE a polygon. Exterior angles are ADJACENT to interior angles and are OUTSIDE the polygon.
If a transversal cuts two parallel lines, and one of the angles formed by this is equal to 83 degrees. What is the measure of the corresponding angles and where are they located in relation to the first angle?
83 degrees
They are located at diagonals from the first angle. You may also have drawn an example, which I will also do on the board.
The measure of an exterior angle to a triangle is equal to the sum of what other angles?
The two nonadjacent interior angles.
I have a 7-sided polygon. Find the sum of the interior angles.
900
I have two similar triangles.
For the small Triangle, the long leg is 10 ft long, while the short leg is x-ft long.
For the big triangle, the long leg is 30 ft long, while the short leg is 24 feet.
Find the length of the short leg on the smaller triangle.
10/30=x/24
240=30x
x=8
What is a transversal line?
A transversal is a line that intersects two parallel lines.
A transversal cuts two parallel lines. A given angle measures 92 degrees. What is the measurement of the supplementary angles and where are they located? (You might want to draw this out)
The supplementary angles measure 88 degrees.
They are located adjacent to the given angle and all of it's corresponding angles. We can draw this out, which I will do on the board.
A triangle has the bottom line extended on the right, to create an exterior angle that measures 123 degrees. The two nonadjacent angles in this triangle equal x, and x+29. What are the measurements of these angles?
x = 47
x + 29 = 76
I have an 8-sided REGULAR polygon. Find the measure of EACH interior angle.
(n-2) * 180 = 1080
Regular polygon means all interior angles are the same, so 1080/8=135
I have two similar triangles.
For the small Triangle, the long leg is x ft long, while the short leg is 8-ft long.
For the big triangle, the long leg is 30 ft long, while the short leg is 20 feet.
Find the length of the long leg on the smaller triangle.
8/20=x/30
240=20x
x=12
What are similar triangles? (2 criteria)
Triangles that:
1. Are made up of the same angles.
2. have sides that are proportional to one another.
A triangle has a 90 degree interior angle. The angle above that is labeled x. The angle to the right of that is labeled y. The bottom line contains both y and the right angle, but also extends beyond the triangle to form an exterior angle. The exterior angle is labeled 115. Find the measures of angles x and y.
x = 25
y = 65
A triangle has measures of (x+2), (x+36), and (x+40). Find the degree measurements of these angles.
X+2 is 36
X+36 is 70
X+40 is 74
I have a 5-sided polygon, with interior angles measuring x, x+60, x+50, x+10, and x. Find the measure of each interior angle
(n-2) * 180 = 540
x+x+60+x+50+x+10+x
84, 144, 134, 94, 84
I have two similar triangles.
For the small Triangle, the long leg is x ft long, while the short leg is 7-ft long.
For the big triangle, the long leg is (x+30) ft long, while the short leg is 10 feet.
Find x.
7/10=x/(x+30)
7(x+30)=10x
7x+210=10x
210=3x
x=70
At each vertex, a triangle has this many adjacent angles.
2. Remember, exterior angles are adjacent.