Mrs. Smith teaching Geometry and wanted to help her students do their best on exams. After failing to find any research on different test formats, she decided to conduct her own research. She flipped a coin for each student in her classes. If the coin
landed heads up, the student took a multiple-choice test. If the coin landed tails up, the student received a fill-in-the-blank
exam. Afterward, Mrs. Johnson compared the averages for the two test formats. What is the variable of interest in this case?
O student scores
O Mrs. Johnson
O test format
O the coin

explanation:

step-by-step explanation:

  b:   ∠x = 28.6°, ∠y = 31.2°, ∠z = 120.2°

step-by-step explanation:

this is one of those questions where "test taking skill" is all you need. the only answer that has angles that sum to 180° is the one shown above. the remaining choices do not describe the angles of a triangle.

if you want to do more work than simply adding the offered numbers, you can also check them against the law of sines. it should be true that

  x/sin(x) = y/sin(y) = z/sin(z)

and all of these ratios must be greater than 15, the longest side length.

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if you want to solve the triangle from scratch, i'd suggest solving for the largest angle using the law of cosines.

  z² = x² +y² -2xy·cos(z)

  z = arccos((x² +y² -z²)/(2xy)) = arccos(-75.11/149.4) = 120.182°

now you can find y from the law of sines

  y = arcsin(y/z·sin(z)) = 31.242°