Triangle abc is rotated 180 about the origin. use complete sentences to describe the relationship between the corresponding angles of triangle abc and its image

Since the transformation occurring is rotation at 180 degrees about the origin, then the resulting image would be a reflection of the original image. Additionally, since the rotation is 180 degrees, then there is a movement of 2 quadrants for the corners A, B and C.

Therefore this would also mean that if point A is in coordinate (x, y) then point A’ would be in coordinate (-x, -y). Similar is true with point B and point C and their corresponding reflection corners point B’ and point C’. So for example if point A is located at (-5, 3) then point A’ must be at (5, -3).

we know that

applying the law of sines

°

so

∠j=18°

∠k=29°

∠l=180-(18+29)=133°

the answer part a) is

the measure of angle k is  ≈29°

part b)  the measure of angle k could also be

(180-29)=151°

so

∠j=18°

∠k=151°

∠l=180-(18+151)=11°

the answer part b) is

the measure of angle k could also be 151°

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