Which relationship is always true for the angles r, x, y, and z of triangle ABC?

A triangle is shown with a leg extending past the top vertex. The vertices are labeled ABC. Angle y is located inside the triangle at vertex B. Angle z is located inside the triangle at vertex C. Angle x is located outside the triangle between beside vertex A and the extended leg. Angle r is located inside the triangle at vertex A.
@paki
x + z = y
180 degrees − x = r
x + y + z = 180 degrees
x + y + z = 90 degrees

Question

Which relationship is always true for the angles r, x, y, and z of triangle ABC?

A triangle is shown with a leg extending past the top vertex. The vertices are labeled ABC. Angle y is located inside the triangle at vertex B. Angle z is located inside the triangle at vertex C. Angle x is located outside the triangle between beside vertex A and the extended leg. Angle r is located inside the triangle at vertex A. 
@paki
 x + z = y 
180 degrees − x = r 
x + y + z = 180 degrees 
x + y + z = 90 degrees

anonymous · Answer

attachment

midhun.madhu1987 · Answer

x + r = 180

What is the reason for this?