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kondaur [170]
3 years ago
6

What’s the indicated measure

Mathematics
2 answers:
Mashutka [201]3 years ago
6 0

<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°



yaroslaw [1]3 years ago
5 0

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


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

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


Combining like terms, we find:

26n - 4 = 360

26n = 364

\boxed{n = 14}


Our answer is n = 14.

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