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polet [3.4K]
3 years ago
7

Solve for the ? angle

Mathematics
1 answer:
daser333 [38]3 years ago
7 0

Answer:

50

Step-by-step explanation:

since all angles add up to 180

and since this is a right triangle the square in the corner is 90 degrees

so 40+90+x=180

130+x=180

subtract 130 from both sides

130-130+x=180-130

x=50

Hope that helps :)

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since we know the total amount split between both in a 18 : 17 ratio is "x", let's divide "x" by (18 + 17) and distribute accordingly to get the amount of each.

\stackrel{Adam~received}{18\cdot \cfrac{x}{18+17}}\qquad \qquad \stackrel{Tom~received}{17\cdot \cfrac{x}{18+17}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{since we know that Adam got "5" more}}{ \stackrel{Adam}{18\cdot \cfrac{x}{18+17}}~~ = ~~\stackrel{Tom}{17\cdot \cfrac{x}{18+17}~~ + ~~5} }\qquad \implies \qquad \cfrac{18x}{35}~~ + ~~\cfrac{17x}{35}+5

\stackrel{\textit{multiplying both sides by }\stackrel{LCD}{35}}{35\left( \cfrac{18x}{35} \right)~~ = ~~35\left( \cfrac{17x}{35}+5 \right)}\implies 18x~~ = ~~17x+175\implies \boxed{x =175} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{Tom~received}{17\cdot \cfrac{x}{18+17}}\implies \cfrac{17(175)}{35}\implies \blacktriangleright 85 \blacktriangleleft

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