Answer:
75
Step-by-step explanation:
Since DY is parallel to FS, this means we have two parallel lines with a transversal (FJ). This makes ∠JDY and ∠JFS corresponding angles, which makes them congruent. ∠J ≅ ∠J by the reflexive property. Since we now have two corresponding angles congruent in the two triangles, and we know that all triangles have a sum of 180°, this means the third corresponding angles must be congruent as well. Since all three angles are congruent in both triangles, the triangles are similar.
This means that the sides are proportional; this tells us that the ratio of DJ to JY will be the same as the ratio of FJ to JS.
The ratio of DJ to JY is
50/42.
The ratio of FJ to JS is (x+50)/(42+63). This gives us the proportion
50/42 = (x+50)/(42+63)
50/42 = (x+50)/105
Cross multiplying, we have
50(105) = 42(x+50)
5250 = 42(x+50)
Using the distributive property, we have
5250 = 42(x)+42(50)
5250 = 42x+2100
Subtracting 2100 from each side,
5250-2100 = 42x+2100-2100
3150 = 42x
Divide both sides by 42:
3150/42 = 42x/42
75 = x
