Question

Find the value of x. Then find the measure of each labeled angle.
(x-50)°

Answer 1

`\underset{in~degrees}{\textit{sum of all interior angles}}\\\\ S = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\[-0.5em] \hrulefill\\ n=4 \end{cases}\implies S=180(4-2)\implies S=360 \\\\[-0.35em] ~\dotfill\\\\ 90+90+x+(x-50)~~ = ~~360\implies 2x+130=360\implies 2x=230 \\\\\\ x=\cfrac{230}{2}\implies x=115\hspace{12em}\stackrel{x}{115^o}\qquad \stackrel{x-50}{65^o}`