What is the value of x?

Question

Five rays are joined to form an irregular pentagon. The exterior angle to each side of the pentagon are given as (4x plus 8)degrees, (5x plus 5) degrees, (6x minus 1) degrees, 3x degrees and (5x plus 3) degrees.

Answer 1

To find the value of \( x \) from the given exterior angles of the pentagon, we start with the fact that the sum of the exterior angles of any polygon is always \( 360^\circ \).

Given the exterior angles of the pentagon as follows:

1. \( 4x + 8 \)
2. \( 5x + 5 \)
3. \( 6x - 1 \)
4. \( 3x \)
5. \( 5x + 3 \)

We need to set up the equation for the sum of these angles:

\[ (4x + 8) + (5x + 5) + (6x - 1) + (3x) + (5x + 3) = 360 \]

Now, combine all the terms:

1. Combine the \( x \) terms: \[ 4x + 5x + 6x + 3x + 5x = 23x \]

2. Combine the constant terms: \[ 8 + 5 - 1 + 3 = 15 \]

Putting it together, the equation becomes:

\[ 23x + 15 = 360 \]

Subtract \( 15 \) from both sides:

\[ 23x = 360 - 15 \] \[ 23x = 345 \]

Now, solve for \( x \):

\[ x = \frac{345}{23} \] \[ x = 15 \]

Thus, the value of \( x \) is

\[ \boxed{15} \]