If △WYX∼△EGF and the scale factor for these triangles is 2, use the properties of similarity to find the measure of ∠W. (1 point)
Since △WYX∼△EGF, we know that the corresponding angles of the two triangles are equal. Therefore, ∠Y = ∠G and ∠X = ∠F.
Since the scale factor for these triangles is 2, this means that the lengths of the sides of △EGF are twice the lengths of the sides of △WYX. Therefore, the angle opposite the longer side in △EGF is equal to the angle opposite the longer side in △WYX.
Since ∠F is the angle opposite the longer side in △EGF, and ∠X is the angle opposite the longer side in △WYX, we can conclude that ∠F = ∠X.
Therefore, the measure of ∠W is equal to the measure of ∠F, which is $\boxed{60°}$ (since in congruent triangles, corresponding angles are equal).
wrong
I apologize for that mistake. Let's correct that.
Since △WYX∼△EGF and the scale factor for these triangles is 2, this means that the ratio of corresponding sides in these triangles is 1:2.
The measure of ∠W can be found by using the properties of corresponding angles in similar triangles. Since ∠W corresponds to ∠E, the measure of ∠W is equal to the measure of ∠E.
Since the scale factor is 2 and the measure of ∠E is 30°, we can find the measure of ∠W by dividing 30° by 2.
∠W = 30° / 2 = 15°
Therefore, the measure of ∠W is $\boxed{15°}$.