In quadrilateral abcd the measures of the angles are represented by measure angle a=6x-2, measure angle b=6x+5, measure angle c=8x+2, and measure angle d=3x+10. Find the measure angle c

Accepted Solution

[tex]\bf \textit{sum of all interior angles in a polygon}\\\\ S = 180(n-2)~~ \begin{cases} n=\stackrel{number~of}{sides}\\[-0.5em] \hrulefill\\ n = \stackrel{quadrilateral}{4} \end{cases} \\\\\\ \stackrel{\measuredangle a}{(6x-2)}~~+~~\stackrel{\measuredangle b}{(6x+5)}~~+~~\stackrel{\measuredangle c}{(8x+2)}~~+~~\stackrel{\measuredangle d}{(3x+10)}~~=~~180(4-2)[/tex][tex]\bf 23x+15=180(2)\implies 23x+15=360\implies 23x=345 \\\\\\ x = \cfrac{345}{23}\implies \boxed{x = 15} \\\\\\ \stackrel{\measuredangle c}{8x+2}\implies 8(15)+2\implies 122[/tex]