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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.

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Very good: I didn't even pay attention to the fact the congruent angles weren't $\;x^\circ\;$ but rather $\;(x+8)^\circ\;$...I suck and it's a great idea I'm not a junior high school teacher. +1 – DonAntonio Jun 14 '14 at 11:10

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