Question 97003
Here's a drawing to see what's going on:


{{{drawing(500,500,-10,10,-10,10,
line(-10,0,10,0),
line(0,0,8,8),
line(0,0,-8,8),
locate(-10,0,A),
locate(0,0,O),
locate(10,0,B),
locate(8,8,D),
locate(-8.2,8,C)
)}}} note: this drawing is not to scale



Here we can see that all of the angles are formed from intersecting lines that meet with AOB. Also, we can see that these angles all add up to 180 degrees (since they are all supplementary)



So that means that the sum of all of the angles is 180


So it can be translated to....


{{{5x+(3x+30)+(2x+10)=180}}}




{{{5x+3x+30+2x+10=180}}} Remove the parenthesis



{{{10x+40=180}}} Combine like terms on the left side



{{{10x=180-40}}}Subtract 40 from both sides



{{{10x=140}}} Combine like terms on the right side



{{{x=(140)/(10)}}} Divide both sides by 10 to isolate x




{{{x=14}}} Divide


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Answer:

So our answer is {{{x=14}}}