Question

This figure is a regular octagon. What is the value of x and what is the value of y?

Answer 1

An important characteristic of octagons, and similarly to any regular polygon, is that their internal angles are the same and, moreover, they have a particular measure depending on the number of sides.

In the case of an octagon, each one of its internal angles is 135°

So, using this fact, notice that

$x=135\text{ dgr}$

Furthermore, we can notice that x° has the same value as the supplementary angle to y°. In a drawing:

So,

$\begin{gathered} x+y=180\text{dgr} \\ \Rightarrow y=180-135=45dgr \end{gathered}$