Angles in Parallel Lines: Using angles in a triangle

ABC is an isosceles triangle.

AB = AC

Angle B equals 55 degrees.

Find the value X.

Since this is an isosceles triangle, angle B and angle C are equal to each other.

$B=C=55$

Therefore we can calculate angle A since the sum of the angles in the triangle equals 180:

$A=180-55-55=180-110=70$

Since angle X is the vertex of angle A, they are equal, hence:

$A=X=70$

$70$

The angles below are between parallel lines.

What is the value of X?

Our initial objective is to find the angle adjacent to the 94 angle.

Bearing in mind that adjacent angles are equal to 180, we can calculate the following:

$180-94=86$
Let's now observe the triangle.

Considering that the sum of the angles in a triangle is 180, we can determine the following:

$180=x+53+86$

$180=x+139$

$180-139=x$

$x=41$

41°

Lines a and b are parallel.

What is the size of angle $\alpha$?

Please note that according to the definition of corresponding angles, the angle $\alpha$corresponds to the angle located on line a and is also within the small triangle created in the drawing.

As we already have one angle in this triangle, we will try to find and calculate the remaining angles.

Furthermore the angle opposite to the angle 62 next to the vertex is also equal to 62 (vertex opposite angles are equal to one other)

Therefore, we can now calculate the missing angle in the small triangle created in the drawing, which is the angle

$\alpha$

$\alpha=180-54-62$

$\alpha=64$

64

Look at the angles formed by parallel lines in the figure below:

What is the value of X?

Given that the three lines are parallel:

The 75 degree angle is an alternate angle with the one adjacent to angle X on the right side, and therefore is also equal to 75 degrees.

The 64 degree angle is an alternate angle with the one adjacent to angle X on the left side, and therefore is also equal to 64 degrees.

Now we can calculate:

$64+x+75=180$

$x=180-75-64=41$

41°

What is the value of X given the angles between parallel lines shown above?

Due to the fact that the lines are parallel, we will begin by drawing a further imaginary parallel line that crosses the 110 angle.

The angle adjacent to the angle 105 is equal to 75 (a straight angle is equal to 180 degrees) This angle is alternate with the angle that was divided using the imaginary line, therefore it is also equal to 75.

In the picture we are shown that the whole angle is equal to 110. Considering that we found only a part of it, we will indicate the second part of the angle as X since it alternates and is equal to the existing X angle.

Therefore we can say that:

$75+x=100$

$x=110-75=35$

35°

Calculate the value of X according to the diagram.

$66$

ABC is an isosceles triangle.

Calculate the value of X.

Impossible to find

ABC is a triangle.

Calculate the size of internal angle A.

$60$

ABC is a triangle.

AB = AC

Angle C1 is equal to 22°.

Calculate the size of angle B2.

$22$°

Calculate the value of X according to the data in the figure.

$70$$$

ABC triangle

Calculate the value of X

$70$

ABC is a triangle.

Angle C2 is equal to 20°.

Angle C3 is equal to 80°.

Calculate the size of angles A2 and B2.

$A2=80,B2=80$

DE is parallel to BC.

Calculate angles C and B using the data in the diagram below.

$B=75,C=65$

Calculate the value of X and Y according to the data given in the diagram.

$X=70,Y=40$

b || a

Calculate x.

66

Can the drawing exist when b,a are parallel?

No

a,b parallel

Find X

21.26

Lines a and b are parallel.

What is the size of angle $\alpha$?

30

Lines a and b are parallel.

Calculate X.

124

Line a is parallel to line b.

Calculate X.

12