Question

Angles in and out of triangles. What angle does a equal? Explain. What angle does b equal? Explain. Explain why x+y+z=180.

Answer 1

See below.

Explanation:

I assume that the dashed lines are parallel.

The side of the triangle that goes from angle y to angle z is a transversal to the parallel lines.

a = y since they are alternate interior angles of parallel lines cut by a transversal.

The side of the triangle that goes from angle x to angle z is a transversal to the parallel lines.

b = x since they are alternate interior angles of parallel lines cut by a transversal.

b + z + a = 180 since altogether they form a straight angle.

Since a = y, and b = x, we substitute y for a and x for b.

b + z + a = 180

x + z + y = 180

x + y + z = 180