The image shows a heptagon (7-sided polygon) with two sides labeled as $40-10x$ and $6x+24$. We are asked to find the value of $x$, assuming the heptagon is regular. In a regular heptagon, all sides have equal length. Therefore, we can set the two side lengths equal to each other and solve for $x$.

1. Problem Description

The image shows a heptagon (7-sided polygon) with two sides labeled as $40-10x$ and $6x+24$. We are asked to find the value of $x$, assuming the heptagon is regular. In a regular heptagon, all sides have equal length. Therefore, we can set the two side lengths equal to each other and solve for $x$.

2. Solution Steps

Since the heptagon is regular, we can equate the expressions representing the side lengths:

$40 - 10x = 6x + 24$

Add $10x$ to both sides of the equation:

$40 - 10x + 10x = 6x + 24 + 10x$

$40 = 16x + 24$

Subtract 24 from both sides of the equation:

$40 - 24 = 16x + 24 - 24$

$16 = 16x$

Divide both sides of the equation by 16:

$\frac{16}{16} = \frac{16x}{16}$

$1 = x$

3. Final Answer

$x = 1$