Line C intersects the sides of triangle ABC: AB at point K, BC at point M angle ABC is 30 degrees angle ACB

Line C intersects the sides of triangle ABC: AB at point K, BC at point M angle ABC is 30 degrees angle ACB is 115 degrees angle AKM is 145 degrees prove that lines C and AC are parallel to line C. Find the outer angle of triangle ABC at vertex A.

We know:
angle ABC = 60 °, angle ACB = 70 °;
Find the BAC angle:
angle BAC = 180 ° – 60 ° – 70 °;
angle BAC = 50 °.
We know:
angle AKM = 130 °;
Find the BKM angle and BAC angle:
angle BKM and BAC = 180 ° – 130 °;
angle BKM and BAC = 50 °;
Find the BMK angle and ACB angle:
angle BMK and ACB = 180 ° – 60 ° – 50 °;
angle BMK and ACB = 70 ° => a || AC.
angle BAC = 50 ° => A = 180 – 50 = 130;