i)

You got the isosceles triangle's base angles mixed up. Those are not the base angles.

BD = CD, not BC = BD

ii)

You've used the wrong pair of lines for the justification of the alternate angles.

Besides that the other pair of lines , (ADand BC), aren't parallel since the question did not specify and it cannot be deduced from the info also.

So this (b) is not solvable right?

You might have to assume ∠FDB is 90°. I've seen this question in some past year paper and the answer key took it to be 90° as well.

That’s way at the answer says. But that’s not correct to assume anything without proof.

My guess is that the setters omitted the right angle marking by mistake.

Turns out this question is from MGS 2019 SA1.

If you're doing this as a practice paper on your own, you may skip part b) , or contact the school for clarification.

If you're doing this as question given by your school then it's best to ask your teachers .