Question

Find the values of x, y, and z. The diagram is not to scale.

x = 83, y = 67, z = 104
x = 86, y = 75, z = 82
x = 86, y = 94, z = 75
x = 80, y = 62, z = 100

Answer 1

Check the picture below.

Answer 2

The correct option is x=80,y=62,z=100

To find the values of x, y, and z, we can use the angles in the triangles and the fact that the sum of angles in any triangle is 180 degrees.

For ΔBAC:

x+36+54=180

x+90=180

x=90−36−54

x=90−90

x=0

For ΔCAD:

18+y+z=180

y+z=180−18

y+z=162

Now, let's check the given options:

x=83,y=67,z=104

x=0 (correct)

y+z=67+104=171 (incorrect)

x=86,y=75,z=82

x=0 (correct)

y+z=75+82=157 (incorrect)

x=86,y=94,z=75

x=0 (correct)

y+z=94+75=169 (incorrect)

x=80,y=62,z=100

x=0 (correct)

y+z=62+100=162 (correct)

Therefore, the correct option is:

x=80,y=62,z=100