Examples with solutions for Angles in Parallel Lines: Generate a random angle

Exercise #1

According to the drawing

What is the size of the angle? α \alpha ?

120

Video Solution

Step-by-Step Solution

Given that the angle
α \alpha is a corresponding angle to the angle 120 and is also equal to it, thereforeα=120 \alpha=120

Answer

120 120

Exercise #2

a is parallel to b.

Calculate the angles shown in the diagram.

115115115111222333444555666777aaabbb

Video Solution

Step-by-Step Solution

Given that according to the definition, the vertex angles are equal to each other, it can be argued that:

115=2 115=2 Now we can calculate the second pair of vertex angles in the same circle:

1=3 1=3

Since the sum of a plane angle is 180 degrees, angle 1 and angle 3 are complementary to 180 degrees and equal to 65 degrees.

We now notice that between the parallel lines there are corresponding and equal angles, and they are:

115=4 115=4

Since angle 4 is opposite to angle 6, it is equal to it and also equal to 65 degrees.

Another pair of alternate angles are angle 1 and angle 5.

We have proven that:1=3=65 1=3=65

Therefore, angle 5 is also equal to 65 degrees.

Since angle 7 is opposite to angle 5, it is equal to it and also equal to 115 degrees.

That is:

115=2=4=6 115=2=4=6

65=1=3=5=7 65=1=3=5=7

Answer

1, 3 , 5, 7 = 65°; 2, 4 , 6 = 115°

Exercise #3

Angle 1 is 20 degrees.

Calculate the size of angle 2.

12

Video Solution

Step-by-Step Solution

Remember the definition of vertically opposite angles:

Vertically opposite angles are formed between two intersecting lines, and they actually have a common vertex and are opposite each other. Vertically opposite angles are equal in size.

Therefore:

1=2=20 1=2=20

Answer

20 20

Exercise #4

Calculates the size of the angle α \alpha

α40

Video Solution

Step-by-Step Solution

Let's review the definition of alternate angles between parallel lines:

Alternate angles are angles located on two different sides of the line that intersects two parallels, and that are also not at the same level with respect to the parallel they are adjacent to. Alternate angles have the same value as each other.

Therefore:

α=40 \alpha=40

Answer

40 40

Exercise #5

Calculate the expression

α+B \alpha+B B30150

Video Solution

Step-by-Step Solution

According to the definition of alternate angles:

Alternate angles are angles located on two different sides of the line that intersects two parallels, and that are also not on the same level with respect to the parallel to which they are adjacent.

It can be said that:

α=30 \alpha=30

β=150 \beta=150

And therefore:

30+150=180 30+150=180

Answer

180 180

Exercise #6

Given two parallel lines

Calculate the angle α \alpha

α125

Video Solution

Step-by-Step Solution

The angle 125 and the angle alpha are vertically opposite angles, so they are equal to each other.

α=125 \alpha=125

Answer

125 125

Exercise #7

Look at the parallelogram in the diagram. Calculate the angles indicated.

3020βα

Video Solution

Step-by-Step Solution

a a is an alternate angle to the angle that equals 30 degrees. That meansα=30 \alpha=30 Now we can calculate: β \beta

As they are adjacent and theredore complementary angles to 180:

18030=150 180-30=150

Angleγ \gamma Is on one side with an angle of 20, which means:

γ=20 \gamma=20

Answer

α=30 \alpha=30 β=150 \beta=150 γ=20 \gamma=20

Exercise #8

a.b parallel. Find the angles marked

ααα104104104818181βββaaabbb

Video Solution

Step-by-Step Solution

In the question, we can see that there are two pairs of parallel lines, line a and line b.

When passing another line between parallel lines, different angles are formed, which we need to know.

 

Angles alpha and the given angle of 104 are on different sides of the transversal line, but both are in the interior region between the two parallel lines,

This means they are alternate angles, and alternate angles are equal.

Therefore, 

Angle beta and the second given angle of 81 degrees are both on the same side of the transversal line, but each is in a different position relative to the parallel lines, one in the exterior region and one in the interior. Therefore, we can see that these are corresponding angles, and corresponding angles are equal.

Therefore,

Answer

α=104 \alpha=104 β=81 \beta=81

Exercise #9

What is the value of X given that the angles are between parallel lines?

XXX154154154

Video Solution

Step-by-Step Solution

The angle X given to us in the drawing corresponds to an angle that is adjacent to an angle equal to 154 degrees. Therefore, we will mark it with an X.

Now we can calculate:

x+154=180 x+154=180

x=180154=26 x=180-154=26

Answer

26°

Exercise #10

a and b are parallel lines.

Calculate the size of angle α \alpha .

aaabbb100α

Video Solution

Answer

100 100

Exercise #11

Angle 2 is equal to 110 degrees.

Calculate the size of angle 1.

12

Video Solution

Answer

70 70

Exercise #12

Calculate angle α \alpha given that the lines in the diagram are parallel.

ααα50

Video Solution

Answer

50°

Exercise #13

Calculate angles α,β \alpha,\beta

αβ5

Video Solution

Answer

α=175 \alpha=175 β=5 \beta=5

Exercise #14

Calculates the size of the angle α \alpha

120α

Video Solution

Answer

60 60

Exercise #15

Calculates the size of the angle α \alpha

20α

Video Solution

Answer

160 160

Exercise #16

Calculates the size of the angle β \beta

Video Solution

Answer

90 90

Exercise #17

Calculates the size of the angle β \beta

170β

Video Solution

Answer

10 10

Exercise #18

Calculate the angles indicated in the figure given that a and b are parallel.

137137137bbbaaaCD

Video Solution

Answer

C-43 D-137

Exercise #19

Calculate the angle α \alpha given that the lines in the diagram are parallel.

ααα55

Video Solution

Answer

125°

Exercise #20

Calculate the angle α \alpha given that the lines in the diagram below are parallel.

ααα40

Video Solution

Answer

40°