Question

The measure of each interior angle of a regular 100-gon is (3x + 26.4).What is the value of x?​

Answer 1

$\bf \textit{sum of all interior angles in a polygon}\\\\ n\theta = 180(n-2)~~ \begin{cases} n = sides\\ \theta =angle~in\\ \qquad degrees\\[-0.5em] \hrulefill\\ n= 100 \end{cases}\implies \theta 100=180(100-2) \\\\\\ 100\theta = 180(98)\implies 100\theta =17640\implies \theta =\cfrac{17640}{100}\implies \theta = \cfrac{882}{5}$

which is pretty much just 176.4°, well, we also know that θ = 3x + 26.4

$\bf 176.4 = 3x + 26.4\implies 150 = 3x\implies \cfrac{150}{3}=x\implies 50=x$