Find the value of x, y and z in the figure. where a = 6, b = 14

A)x = 33°, y = 94°, z = 53°
B)x = 33°, y = 53°, z = 94°
C)x = 94°, y = 94°, z = 53°
D)x = 33°, y = 53°, z = 53°
E)x = 60°, y = 60°, z = 60°

Question

Find the value of x, y and z in the figure.​  ​ where a = 6, b = 14
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A)​x = 33°, y = 94°, z = 53° 
B)​x = 33°, y = 53°, z = 94° 
C)​x = 94°, y = 94°, z = 53° 
D)x = 33°, y = 53°, z = 53° 
E)​x = 60°, y = 60°, z = 60°

Quizplus · Accepted Answer

First, we can find x by using the fact that angles on a straight line add up to 180 degrees. We know that x+y = 147 degrees (complementary angles) and z+y = 147 degrees (vertical angles), so x+z+2y = 294 degrees. We also know that z+y = 147 degrees and z+x = 90 degrees (since z is a complement to angle A). Therefore, x+z = 90 degrees and x = 90-z. Substituting into our previous equation gives 90-z+z+2y = 294, or 2y = 204 and y = 102.
Now we know that x = 90-z and y = 102. We can use the fact that angles in a triangle add up to 180 degrees to find z. The triangle with sides of length 6, 14, and 16 is a right triangle (since 6^2 + 14^2 = 196 = 16^2), so angle A is a right angle (90 degrees). Therefore, z+90+arctan(14/6) = 180, or z+90+67.38 = 180. Solving for z gives z = 22.62 degrees. Therefore, x = 67.38 degrees, y = 102 degrees, and z = 22.62 degrees, which matches answer choice B.

Find the Value of X, Y and Z in the Figure.​

Find the Value of X, Y and Z in the Figure.