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
​
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

By applying the angle sum property of triangle and using the values of a and b given in the figure, we can find the angles x, y and z as follows:

x + y + z = 180° (angle sum property of triangle)
x + 2z = 180° (since angle BAD is a straight line)
y + 2x = 180° (since angle ADC is a straight line)
a + 2b + x + y = 360° (sum of exterior angles of polygon ABCDE)
6 + 28 + x + y = 360° (substituting the values of a and b)
x + y = 326°

Solving the above equations simultaneously, we get:
x = 33°, y = 53°, z = 94°

Therefore, the best choice is B.

Find the Value of X,y and Z in the Figure