Question

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Answer 1

Answer:

$x$ = 12

Step-by-step explanation:

The shape ABCDEF is an irregular polygon.  

The sum of the interior angles of any regular or irregular polygon = (n - 2) x 180 (where n is the number of sides of the polygon).  

Therefore, the sum of the interior angles of shape ABCDEF = (6 - 2) x 180 = 720°

So to find the value of $x$, we need to add together all the interior angles and equal it to 720, then solve for $x$.

Before we do that, we need to determine angle F.

From inspection, we can see that angle F and 52° are a linear pair.  We know that a linear pair of angles add up to 180°, so F + 52 = 180  ⇒  F = 180 - 52 = 128°

Therefore:

                                           A + B + C + D + E + F = 720

(10$x$ - 5) + 108 + (8$x$ - 3) + (14$x$ - 25) + 133 + 128 = 720

Collect like terms:

10$x$ + 8$x$ + 14$x$ - 5 + 108 - 3 - 25 + 133 + 128 = 720

Combine like terms:

32$x$ + 336 = 720

Subtract 336 from both sides:

32$x$ = 384

Divide both sides by 32:

$x$ = 12