Can someone me understand this and show work

So first off, the most important thing in Geometry is to know the relationship between angles and lines. A vertical line is 180 degrees, a line bisecting something means that whatever is bisected is equal to the other side, vertical angles are equal to each other, etc. Once you understand these it will be a breeze. Make sure you always write down the numbers you find out on the problem in its place so you can keep on track and visualize it better!

8) The 2 angles represented by the equations are being bisected by a vertical line. So that means they are equal to each other and we can solve by putting that into an equation. 5x-46=2x+5, 3x-46=5, 3x=51, x=17. Now just plug in 17 for x. 5(17)-46, 85-46=39. <PQR=39

9) A linear pair is just 2 angles that make a 180 degree angle so, 1, 4, & 5

10) A vertical angle is an angle that is equal and opposite to the other. In this case the only clear one is 1 & 4 (Answer) but angles 2 and 3, when added, would equal angle 5.

11) Supplementary means it equals 180 degrees so the same as #9. 1 & 5, 4 & 5

12) Set 3x+20 and y-20 have different variables, it is easier to use x and 3x+20.Both of these angles form a linear pair, which means they equal 180 so set both of them equal to it. 3x+20+x=180. Combine like terms. 4x+20=180, 4x=160, x=40. Now plug in 40 for x. Since one angle is just x and x=40, subtract that from 180 to find the other angle. We now know y-20=140 so we can simply work out the equation. y-20=140, y=160. Our final answer is x=40 and y=160.

13) (sorry its too blurry I can't risk it but i'm sure you get it now) Just set the angles equal to each other to find the first angle and subtract the angle from 180 to get the other angle.

14) Line AOC equals 180 so that means if <AOB =90 then <BOC equals 90. Line BOE is also a supplementary angle meaning if we add up all the numbers we now know on the line (90,75) they would equal 165. 180-165= 15 meaning <COD=15 degrees. Since <COD is 15 and <DOE is 75 we can add those up and subtract it from 180 (then add 75 again) to find <AOD. 75+15=90 (right angles are 90). 90+75=165, so <AOD=165 degrees.

I hope I didn't get anything wrong I was in a bit of a rush. Just remember the rules and the relationships and you'll do great!

d is correct

step-by-step explanation:

19.side- angle- side

20. angle- side- angle

step-by-step explanation: