2x + 10 and x + 40 are vertical angles. By definition, vertical angles are congruent. So let's take care of that first. 2x+10 = x+40. Subtract an x from both sides and at the same time subtract 10 from both sides to get x = 30. Ok so x = 30. So what, right? We need y. Well, 2y+x is vertical with an angle that has the exact same measure as 2y+x because vertical angles are congruent. We know that all those angles add up to equal 360, so here's our equation: [tex]2x+10+x+40+2y+x+2y+x=360[/tex]. Combining like terms gives us 5x+4y=360. We already have a value for x, remember, so we will sub it in. x=30. 5(30)+4y=360 and 150 + 4y = 360. Subtract 150 from both sides and we have 4y = 210. Divide both sides by 4 to get that y = 52.5. There you go!
