Question

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

Answer 1

`\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)`

`\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`

Answer 2

c = 122 degrees

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