Trigonometry - how to find angles of triangle within another triangle?

Question

What are the angles of angle 1 and 2?

I don't see how any of them could be corresponding angles...

The adjacent side of angle 2 is parallel to the hypotenuse of the bigger triangle, just to make it clear.

Answer 1

Here is a picture that will hopefully explain why Angle 1 is $20^\circ$.

If you solve for $\angle 1$ from the equation $$70^\circ + \angle 1 + 90^\circ = 180^\circ,$$ you will find that $\angle 1 = 20^\circ$.

Answer 2

Given:$\angle A=20, \angle ACB=90, \angle EBD=90$

$\angle ABC+\angle CBD +\angle EBD=180\Rightarrow 70+\angle CBD+90=180 \Rightarrow \angle CBD=20$

Given:$\angle BDC=90 \Rightarrow \angle BCD+\angle CDB+\angle CBD=180$(sum of 3 angles of triangle=180)

$\therefore \angle BCD=70$