Angles in Parallel Lines: Three parallel lines

We will mark the angle opposite the vertex of 38 with the number 1, therefore, angle 1 is equal to 38 degrees.

We will mark the angle adjacent to angle $\beta$ with the number 2. And since angle 2 corresponds to the angle 140, angle 2 will be equal to 140 degrees

Since we know that angle 1 is equal to 38 degrees we can calculate the angle$\alpha$ $\alpha=180-38=142$

Now we can calculate the angle$\beta$

180 is equal to angle 2 plus the other angle$\beta$

Since we are given the size of angle 2, we replace the equation and calculate:

$\beta=180-140=40$

In the drawing before us, we can see three parallel lines and two lines that intersect them.

We are asked to find the size of angle ABC,

We can identify that the angle is actually composed of two angles, angle ABH and CBH.

In fact, we will calculate the size of each angle separately and combine them.

Angle A is an alternate angle to angle ABH, and since alternate angles are equal, angle ABH equals 92.

Angle CBH is supplementary to angle DCB, supplementary angles equal 180, therefore we can calculate:

$HBC = 180-DCB$

$HBC = 180 - 131$

$HBC = 49$

Now that we have found angles ABH and CBH, we can add them to find angle ABC

$ABH + CBH = ABC$

$92 + 49 = 141$

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:

$64+x+75=180$

$x=180-75-64=41$