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°.
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°
3 answers
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°
25°
65°
100°
50°
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°.
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°.