Question

In the figure, AB←→∥CD←→AB↔∥CD↔. Find x and y.

Answer 1

y = 140 degrees
x = 52 degrees

Answer 2

`x=52\\y=140`

Explanation:

First we will solve
`x`with the interior angles of a triangle rule which is:

The sum of all 3 interior angles in a triangle is 180(α+β+Ф=180)

For this triangle we have already 2(90 and 38) out of 3 angles so we can solve for the remaining angle like this:

`\alpha+\beta+\theta=180\\90+38+x=180\\x=180-90-38\\x=52`

Second we will solve for the
`y` using the same angle
`x` that we found because the line CD is parallel to AB so the smaller triangle is similar (the same shape but different size) to the bigger one and it has the same angles.

The
`x` angle plus
`y-12` will be 180 because they are both supplementary angles (two angles that sum to a straigh angle). We can build the equation to solve
`y` like this:

`52+y-12=180\\y=180-52+12\\y=140`