Question

Decide whether the triangles are similar. If so, determine the appropriate expression to solve for x. Triangles ABC and EDF; triangle ABC has angle A measuring 53 degrees, angle C measuring 62 degrees, side AC labeled as y, side AB labeled as w, and side BC labeled as x; triangle EDF has angle D measuring 61 degrees, angle F measuring 53 degrees, side DE labeled z, side EF labeled u, and side DF labeled r.

Answer 1

Answer:

The answer is "ΔABC ~ ΔEDF; x equals r times w over z "

Step-by-step explanation:

In the given question an attached file is missing. so, please find the file and its solution:

Given:

∠A = 47

∠C= 62

∠D = 71

∠F= 47

In the given triangles equation it closed by the angle to angle, while all 3 types are consistent.  

In the triangle ABC  and the DEF:

⇒∠A+ ∠B+∠C =180         and                 ⇒∠D+ ∠E+∠F =180

⇒∠B+ 109 =180                                       ⇒∠F+ 118  =180

⇒∠B= 71                                                   ⇒∠B= 62

On comparing the Δ ABC and  Δ EDF

∠A=∠E

∠B=∠D

∠C=∠F

So,

$\to \frac{x}{r} = \frac{w}{z}\\\\\boxed{\to x = r \times \frac{w}{z}}$