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. x + z = y 180 degrees − x = r x + y + z = 180 degrees x + y + z = 90 degrees

Answer 1

y+z=x

Step-by-step explanation:

we know that

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

Hope This Helps!

Answer 2

Answer: (180 degrees − x = r)

Explanation:

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