Question

Find the value of x if the figure is a regular polygon.

Answer 1

taking a peek at this regular polygon hmm is has 6 sides, so is a hexagon, ok.

`\textit{sum of all interior angles in regular polygon}\\\\ n\theta =180(n-2)~~ \begin{cases} n=\stackrel{number~of}{sides}\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ n=6 \end{cases}\implies 6\theta =180(6-2) \\\\\\ 6\theta =180(4)\implies 6\theta =720\implies \theta =\cfrac{720}{6}\implies \boxed{x=\theta =120}`