Decide whether the triangles are similar. if so, determine the appropriate expression to solve for x.

triangles abc and edf, where triangle abc has angle a measuring 47 degrees, angle c measuring 62 degrees, side ac labeled as y, side ab labeled as w, and side bc labeled as x and triangle edf has angle d measuring 71 degrees, angle e measuring 47 degrees, side de labeled z, side ef labeled u, and side df labeled r

the triangles are not similar; no expression for x can be found.
δabc ~ δdef; x equals r times w over u
δabc ~ δedf; x equals r times w over u
δabc ~ δedf; x equals r times w over z

Step-by-step explanation:

The given triangles are similar by Angle-Angle postulate, because all three pairs of corresponding angles are congruent.

Triangle ABC

Triangle DEF

As you can see,

Therefore, triangles are similar, that is

From the similarity, we deduct the following proportions

According to the problem,  

From proportions, we have

Therefore, the right answer is the last choice.

Δ ABC is similar to Δ EDF and

Step-by-step explanation:

In Δ ABC, ∠ A = 47° and ∠ C = 62°  

So, ∠ B = 180° - 62° - 47° = 71°

Again, in Δ EDF, ∠ D = 71°, and ∠ E = 47°  

So, ∠ F = 180° - 71° - 47° = 62°

Hence, Δ ABC is similar to Δ EDF

Now, for two similar triangles the ratio of corresponding sides will be in the same ratio.

So,

⇒

⇒ .

Therefore, the correct option is 3. (Answer)

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