Question

What’s the indicated measure

Answer 1

<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°

Answer 2

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.