This is a relatively complex problem and it took me a good 20 minutes to solve, I included a sketch I made myself while im solving this problem hope it helps with the explanation. (the dotted lines are my drawings, also I labeled the points just look at my graph)
Now to find <x, we can use the exterior angles theorem a couple of times.
<x=<p+<AGE
<x=30 degrees + <AGE
Now use the theorem again to find <AGE
<AGE=<q+<BIG
Now use substitution for <q and for <AGE
<x=30 degrees+60 degrees+ <BIG
We put this to the side for now and try solve for <CHD which is not very difficult
<CHD=180-45-20=115
We can also clearly figure out <HFI using vertical angles theorem.
<HFI=<Y
Because they all form a triangle we can conclude that <y+<BIG=180 degrees-<FHI= 180-115=65 degrees
substitution again
<x+<y=30+60+<BIG+<HFI (remember <HFI = <y vertical angles theorem)
<x+<y=30+60+65 (remember how we did before these 2 angles adds up to 65?)
<x+<y=155 degrees
Now please don't hate me on this, I'm sure there is more efficient ways to explain this problem, this is just my way from trial and error.
<u>Tip for next time you are stuck on a geometry problem, don't be afraid to draw the graph again on paper and add lines to it!</u>
<u>You won't get everything perfect the first time you try but the more you practice the more comfortable you are with these problems, Hope my explanation helped!</u>
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**Just a note would you mind telling me where you got this problem form, its pretty challenging :)
