Question

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)

25°

65°

100°

50°

Answer 1

[AI-generated answer — Bot GPT 3.5]

The measure of ∠W can be found using the property that corresponding angles of similar triangles are equal.

Since the scale factor for these triangles is 2, this means that corresponding sides are in a 1:2 ratio.

Given that ∠Y = 50°, we can write an equation for ∠W:

∠W = ∠Y + ∠X
∠W = 50° + ∠X

Since ∠X corresponds to ∠F in triangle EGF, we can set up a proportion:

∠X/∠F = 1/2
∠X/65° = 1/2
∠X = 65°/2
∠X = 32.5°

Therefore, ∠W = 50° + 32.5° = 82.5°

So, the measure of ∠W is 82.5°.

Answer 2

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)

25°

65°

100°

50°

Answer 3

[AI-generated answer — Bot GPT 3.5]

Since △WYX∼△EGF and the scale factor is 2, this means that the corresponding angles of the triangles are equal.

Given that ∠F = 100° in triangle EGF, we can find the measure of ∠W in triangle WYX.

∠W = ∠Y + ∠X

We know that ∠Y corresponds to ∠E, so ∠Y = ∠E = 100°.

Since the sum of angles in a triangle is 180°, we can find ∠X:

∠X = 180° - ∠Y - ∠W
∠X = 180° - 100° - ∠W
∠X = 80° - ∠W

These angles correspond to each other in similar triangles, so:

∠X / ∠W = 1 / 2
80° - ∠W / ∠W = 1 / 2
80° - ∠W = (1/2)∠W
80° = (3/2)∠W
∠W = 80° * (2/3)
∠W = 160 / 3
∠W ≈ 53.333°

Therefore, the measure of ∠W is approximately 53.333°.