Lines AB and CD (if shown) are straight lines. Find x. Give reasons to justify your solutions. PLEASE ANSWER ASAP!!!

X=20 degrees

Step-by-step explanation:

    So, questions like this are not so hard if you break it up into little chunks. Remember that there are 360 degrees in a circle, and your group of triangles make up a 'circle' where your total degrees should equal 360.

    First, you need to find the blank of measure of angle DOB equals measure of DOE plus the measure of angle EOB. This is the other angle that fits into the bigger angle DOB. The reasoning behind that would be that they are corresponding angles. They are on the same side and share the side OE.

    Second you need to fill in the blank measure of angle DOB equals DOE plus x. This is already explained as substitution because you took away the angle sign from DOE and X, but the sentence is still true.

    Third, you need to fill in the measure of angle AOC is equal to the measurement of angle COB because they are Vertical angles. They look like they are 'on top' of each other.

    Forth you need to fill in AOD equals COB plus x. This is substitution because you substituted AOD for COB since you just proved they are the same measurement.

    Fifth you answer what x equals, because you have proved everything you need to at this point. angle AOD plus 110 degrees equals 180 degrees, since that is a flat angle, so you can solve for angle AOD and get that it equals  70 degrees. Then, since you know that angle COB equals angle AOD you can substitute 70 degrees for angle COB. Next, you can solve for x, knowing that angle COB plus angle X equal angle DOE, which is a right angle, so angle DOE equals 90 degrees. So, 90 degrees minus angle COB equals x. So, 90-70 which is angle COB, equals 20, so x is 20 degrees.

You're welcome :)