A quadrilateral is inscribed in a circle. Find the measure of each missing angle as labeled below. Show your work and/or explain how you got your answer. 1 point for each correct angle measure and 1 point for explaining or showing how you got your answer. Don’t forget to label your answers.

C = 95°

D = 72°

F = 108°

Step-by-step explanation:

Opposite angles of an inscribed quadrilateral are supplementary. Inscribed angles are half the measure of the arc they subtend. (The latter statement can be used to prove the former one.)

Using these relations, we have .

 C = 180° -E = 180° -85° = 95°

 D = 144°/2 = 72°

 F = 180° -D = 180° -72° = 108°

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step-by-step explanation:

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.