Question

Which relationship is always true for the angles x, y, and z of triangle ABC? (4 points)

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 side AC and the extended leg.
x + z = y
y + z = x
x + y + z = 180 degrees
x + y + z = 90 degrees

Answer 1

y + z = x

Explanation:

exterior angle is the sum of other two interior angles.

Answer 2

y+z=x

Explanation:

The Exterior Angle Property of a Triangle states that the measure of exterior angle of a triangle is equals to the sum of measures of its interior opposite angles

In this problem

Angle y and angle z are interior angles of triangle ABC and angle x is a exterior angle of triangle ABC

therefore

Applying the Exterior Angle Property of a Triangle

y+z=x