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qabtt

We know that the interior angles of the polygon is 360 degrees, given to us by the formula [tex] 180(n - 2) [/tex], where [tex] n [/tex] is the number of sides of the shape.


Thus, all interior angles must sum to 360 degrees. By this we can calculate [tex] n [/tex]:

[tex] 4n + (5n + 6) + (8n - 12) + (9n + 2) = 360 [/tex]


Combining like terms, we find:

[tex] 26n - 4 = 360 [/tex]

[tex] 26n = 364 [/tex]

[tex] \boxed{n = 14} [/tex]


Our answer is n = 14.

choixongdong

<A + <B + <C + <D = 360

where

<A = 4n

<B = 9n + 2

<C = 8n - 12

<D = 5n + 6

So

4n + 9n + 2 + 8n - 12 + 5n + 6 = 360

combine like terms

26n - 4 = 360

Add 4 to both sides

26n = 364

Divide both sides by 26

n = 14


Substitute n = 14 into those below to find measure of each:

<A = 4n = 4 *14 = 56

<B = 9n + 2 = 9*14 + 2 = 128

<C = 8n - 12 = 8*14 - 12 = 100

<D = 5n + 6 = 5*14 + 6 = 76


Answer:

n = 14

<A = 56°

<B = 128°

<C = 100°

<D = 76°



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