Best answer gets

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

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

yes

Step-by-step explanation:

they are the same shape and have the same angles

Answer : The correct option is, ΔABC ΔFDE; x equals z times w over r

Step-by-step explanation :

Condition of similar triangles are:

If two corresponding angles are equal.

If three corresponding sides are in same ratio.

The ratio of two pairs of corresponding sides are equal and their included angle are equal.

In given ΔABC and ΔDEF,

∠A = ∠F    (equal to 53°)

∠B = ∠D    (equal to 65°)

In this two corresponding angles are equal. So, these triangles are similar.

The name of similar triangles are,

So,

Thus,

Hence, the correct option is, ΔABC ΔFDE; x equals z times w over r

x = 23.78

step-by-step explanation: