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Liula [17]
3 years ago
7

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
Mathematics
2 answers:
OleMash [197]3 years ago
8 0

\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

balandron [24]3 years ago
7 0

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

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Ilia_Sergeevich [38]

The perimeter of the given rectangle will be ( 12x + 10 ).

<h3>What is the perimeter?</h3>

The perimeter is defined as the sum of all the sides of the given shape. For a triangle, the perimeter will be the sum of all the sides of the rectangle.

It is given that the two sides of the rectangle are (2x + 2) and (4x + 3). Then the perimeter of the rectangle will be calculated as below:-

Perimeter =  Sum of all the sides of the rectangle

Perimeter = 2 ( 2x + 2 + 4x + 3 )

Perimeter = 4x + 4 + 8x + 6

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Therefore, the perimeter of the given rectangle will be ( 12x + 10 ).

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Answer:

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Step-by-step explanation:

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<em>Hope this helps</em>

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