Respuesta :
[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]
Answer:
c = 122 degrees
Step-by-step explanation:
A quadrilateral is a shape bounded by four sides. It has four angles too. The sum of the angles in the quadrilateral is 360 degrees. From the information given above, the four angles of the quadrilateral are angle a, angle b, angle c and angle d.
The sizes of the angles are
angle a = 6x-2 degrees
angle b = 6x+5 degrees
angle c= 8x+2 degrees
angle d = 3x+10 degrees
Sum of the angles = 360. Therefore,
6x-2+6x+5 +8x+2 +3x+10 = 360
= 6x + 6x + 8x + 3x = 360 -5-10
23x = 345
x = 350/23 = 15
Angle c = 8x+2 = 8×15 +2 = 122 degrees
