How do I find this angle?

Question

Okay, I know the angles next to $115^{\circ}$ are supplementary to it, so the angles are $65^{\circ}$. I subtracted $65$ and $30$ from $180$ to get to measure angle of $85^{\circ}$. How can I find $e$ this way? Do I use alternate or supplementary angles?

Answer 1

In a triangle, sum of two interior angles is equal to the exterior angle that has no neighbourhood to the interior angles summed up. So we have $$34^\circ+e = 85^\circ \implies e = 51^\circ$$

Answer 2

Hint:

Look at the triangle having the angles $e$ and $34^\circ$. The third angle in that triangle should be easy to calculate, then use the fact that the sum of the angles is $180^\circ$.

Answer 3

You can take out the supplement of 85°, which is 95°. Now you can find the other angle of the triangle that has angles 65° and 34°, which is 81°, and then take its supplement (99°). Now $$e+99^\circ+115^\circ+95^\circ=360^\circ$$ $$e=51^\circ$$