Angles in Parallel Lines: Generate a random angle

a is parallel to b.

Calculate the angles shown in the diagram.

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

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

$1=3$

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:

$115=4$

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:$1=3=65$

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:

$115=2=4=6$

$65=1=3=5=7$

1, 3 , 5, 7 = 65°; 2, 4 , 6 = 115°

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

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:

$x+154=180$

$x=180-154=26$

26°

Calculates the size of the angle $\alpha$

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:

$\alpha=40$

$40$

Given two parallel lines

Calculate the angle $\alpha$

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

$\alpha=125$

$125$

Angle 1 is 20 degrees.

Calculate the size of angle 2.

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:

$1=2=20$

$20$

Calculate the expression

$\alpha+B$

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:

$\alpha=30$

$\beta=150$

And therefore:

$30+150=180$

$180$

According to the drawing

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

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

$120$

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

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

As they are adjacent and theredore complementary angles to 180:

$180-30=150$

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

$\gamma=20$

$\alpha=30$ $\beta=150$ $\gamma=20$

What is the size of the missing angle?

100°

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

50°

Calculate X given that the lines in the diagram below are parallel.

110

Calculate the size of the missing angle given that lines a and b are parallel.

64

Calculate the missing angle given that lines a and b are parallel.

64

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

40°

The lines $a$ and $b$ are parallel.

What is the value of the angle $C$?

137°

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

125°

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

60°

The lines a and b are parallel.

Calculate the angle indicated in red.

118

The lines shown below are parallel.

Calculate the size of angle $\alpha$ and indicate the relationship between the two angles.

110, co-interior angles.

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

C-43 D-137