50 points! Look at the picture attached. Random answers will be reported

Points a, b, and c form a triangle. complete the statements to prove that the sum of the interior angles of triangle abc is 180

1- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis.2- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in the first question?

If cos(2x) = tan^2(y), show that cos(2y) = tan^2(x).