Triangle apparently has two equivalent angles, but not really

Question

What angles are ${a, b, c, d}$? As far as I know, $a = 180^\circ - 130^\circ = 50^\circ$, however, I expected $c$ to be the same as $a$ and it's not, according to cimt.org.uk.

(Figure from cimt.org.uk)

Answer 1

the sides marked with two stripes are equal, which makes the other one the base. Angles adjacent to the base are equal. So b and c are equal. As $a = 50$, and the sum of the angles of a triangle is 180, that makes angles $ b = c = (180 - 50):2 = 65 $ so the angle $ d = 180 - 65 = 115$