Michael and jacob are standing on two docks that are 20 miles apart. they are watching a ship that is out in the ocean. the angle between the dock and the line connecting michael and the ship is 48°, and the angle between the other dock and the line connecting jacob and the ship is 37°. if the ship can travel to either dock, which dock would be closest? explain your answer. a.) michael’s dock would be closer because the angle opposite is smaller. b.) jacob’s dock would be closer because the angle opposite is smaller. c.) michael’s dock would be closer because the docks are 20 miles apart. d.) jacob’s dock would be closer because the docks are 20 miles apart.

A.) Michael’s dock would be closer because the angle opposite is smaller.

Step-by-step explanation:

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq

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'.