Question

A polygon with 5 sides is shown with its exterior angles. The exterior angles are 62 degrees, 66 degrees, 77 degrees, 59 degrees, and (12 x) degrees.
What is the value of x?

6
8
10
12

Answer 1

To find the value of \( x \) in the exterior angle \( 12x \) of a polygon with 5 sides, we can make use of the fact that the sum of the exterior angles of any polygon is always \( 360 \) degrees.

Given the exterior angles of the polygon as follows:
- \( 62^\circ \)
- \( 66^\circ \)
- \( 77^\circ \)
- \( 59^\circ \)
- \( 12x \) degrees

We can set up the equation for the total sum of the exterior angles:

\[
62 + 66 + 77 + 59 + 12x = 360
\]

First, we calculate the sum of the known angles:

\[
62 + 66 = 128
\]
\[
128 + 77 = 205
\]
\[
205 + 59 = 264
\]

Now we plug this sum into the equation:

\[
264 + 12x = 360
\]

Next, we isolate \( 12x \):

\[
12x = 360 - 264
\]
\[
12x = 96
\]

Now, we solve for \( x \):

\[
x = \frac{96}{12} = 8
\]

Thus, the value of \( x \) is \( \boxed{8} \).