Question

5 the degree measure of each exterior angle of a regular octagon is represented by the expression 7x - 4. solve for x.

Explanation:

Step1: Recall exterior - angle formula for regular polygon

The sum of exterior angles of any polygon is $360^{\circ}$. For a regular octagon (8 - sided polygon), each exterior angle $\theta$ is given by $\theta=\frac{360^{\circ}}{n}$, where $n = 8$. So, each exterior angle of a regular octagon is $\frac{360}{8}=45^{\circ}$.

Step2: Set up the equation

We are given that the measure of each exterior angle is $7x - 4$. So, we set up the equation $7x-4 = 45$.

Step3: Solve the equation for x

Add 4 to both sides of the equation: $7x-4 + 4=45 + 4$, which simplifies to $7x=49$.
Then divide both sides by 7: $\frac{7x}{7}=\frac{49}{7}$, so $x = 7$.

Answer:

$x = 7$