## What is the value of x? Enter your answer in the box. units Triangle F J S with line segment D Y parallel to segment F S with D between

Question

What is the value of x? Enter your answer in the box. units Triangle F J S with line segment D Y parallel to segment F S with D between F and J and Y between S and J. F D equals x. D J equals 50. S Y equals 63. Y J equals 42.

0

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

2. 75 just took the test.