Question

1. the diagram shows a regular polygon. what is the value of x? write your answer as an integer or as a decimal rounded to the nearest tenth. x = ° 18. the diagram shows a regular polygon. what is the value of x? write your answer as an integer or as a decimal rounded to the nearest tenth. x = °

Explanation:

Question 17

Step1: Identify the polygon type

The diagram shows a regular hexagon (6 - sided polygon). For a regular polygon, the formula for the measure of each interior angle is $\frac{(n - 2)\times180^{\circ}}{n}$, where $n$ is the number of sides.

Step2: Substitute $n = 6$ into the formula

Substitute $n = 6$ into $\frac{(n - 2)\times180^{\circ}}{n}$:
\[

$$\begin{align*} \frac{(6 - 2)\times180^{\circ}}{6}&=\frac{4\times180^{\circ}}{6}\\ &=\frac{720^{\circ}}{6}\\ & = 120^{\circ} \end{align*}$$

\]

Step1: Identify the polygon type

The diagram shows a regular pentagon (5 - sided polygon). For a regular polygon, the formula for the measure of each interior angle is $\frac{(n - 2)\times180^{\circ}}{n}$, where $n$ is the number of sides.

Step2: Substitute $n = 5$ into the formula

Substitute $n = 5$ into $\frac{(n - 2)\times180^{\circ}}{n}$:
\[

$$\begin{align*} \frac{(5 - 2)\times180^{\circ}}{5}&=\frac{3\times180^{\circ}}{5}\\ &=\frac{540^{\circ}}{5}\\ & = 108^{\circ} \end{align*}$$

\]

Answer:

$x = 120$

Question 18