Question

Line p is parallel to line q. Which proof explains why the sun of the interior angles of the triangle must be 180

Answer 1

Answer:

We consider a triangle ABC as attached in the answer.

We draw a line parallel to AB that passes  through point C.

Angles C and C' are vertical angles,  therefore ∠C = ∠C'.  

Angles B and B' are corresponding angles,  therefore ∠B = ∠B'.

Angles A and A' are corresponding angles, therefore ∠A = ∠A'.

it can be seen that angle sum ∠A + ∠B + ∠C is equal to the angle sum ∠A' + ∠B' + ∠C'.

The three angles A', B', and C' form together a straight angle  so, their angle sum is 180°. But then the angle sum ∠A + ∠B + ∠C must also be 180°.

This proofs that sum of angles of a triangle is equal to 180.