Question

Which relationship is always true for the angles 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 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:

Let's rename angle BAC to w. Now, we have four angles: w, x, y, and z. We know that w + y + z has to equal 180 degrees, because a triangle's three angels always adds up to 180 degrees. We also know that w + x equals 180 degrees, because they are on the same line. These two phrases are equal:

w + y + z = w + x

We can then cancel w on each side:

y + z = x

Hope this helps! :)