The angle below is the image formed when a figure containing angle, E, F, G∠EFG is dilated by a scale factor of start fraction, 2, divided by, 3, end fraction
3
2
. What is the measure of angle, E, F, G∠EFG?
E'
F'
G'
144°
Answer
Attempt 1 out of 2
m, angle, E, F, G, equalsm∠EFG=
degrees
∘
Since the figure is dilated by a scale factor of 2/3, the measure of angle EFG is also diluted by this factor.
Let's say the measure of angle EFG in the original figure is x degrees.
After dilation, the measure of angle EFG in the image would be (2/3)x degrees.
Therefore, the measure of angle EFG in the image is (2/3)x degrees.
However, the provided answer of 144° suggests that the measure of angle EFG is 144°.
Therefore, (2/3)x = 144°.
To find x:
Multiply both sides of the equation by 3/2:
(3/2)(2/3)x = (3/2)(144°)
x = 216°
So, the measure of angle EFG is 216°.