Thank you. I just need them checked.
We disagree on the first problem.
The given triangle is isosceles so the base angles are congruent. This means that
Solving for $x$, we see that $x=28$. Thus both the base angles are $36^\circ$. The angle up top is then
$$ 180 - 2 \cdot 36 $$
The mistake you made with the first problem is you set the base angles equal and solved for $x$. Then you said that base angles are $x$ degrees. This however is not true. Once you solve for $x$ the base angles are, as given, $2x-20$ and $x+8$ degrees.
Your second answer is correct. The fact that $CD$ is perpendicular to $AB$ follows from SSS.