Final answer:
The measure of angle W'X'Y' after the figure with angle WXY is dilated by a scale factor of 5 is still 129°, as angle measures remain constant through dilation.
Step-by-step explanation:
The student has asked about the measure of an angle after a figure is dilated by a scale factor. Specifically, they mentioned a figure with angle ∠WXY being dilated by a scale factor of 5 to form a new figure with angle ∠W′X′Y′. The question asks to find the measure of ∠W′X′Y′ given that the measure of ∠WXY is 129°.
When a figure is dilated, the sizes of the sides change proportionally according to the scale factor, but the measures of the angles remain the same. This is a fundamental property of similar triangles: corresponding angles in similar triangles are congruent. Therefore, even after dilation, the measure of angle ∠WXY will be equal to the measure of angle ∠W′X′Y′. The measure of ∠W′X′Y′ after the dilation with a scale factor of 5 is still 129°, the same as the measure of ∠WXY before the dilation.