Question

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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 = \boxed{}^\circ

Explanation:

Step1: Identify the polygon type

The diagram shows a regular pentagon (5 - sided polygon). For a regular polygon with \( n \) sides, the measure of each interior angle \( I \) is given by the formula \( I=\frac{(n - 2)\times180^{\circ}}{n} \). Here, \( n = 5 \).

Step2: Calculate the interior angle

Substitute \( n = 5 \) into the formula:

$$
LATEXBLOCK0
$$

Step3: Find the exterior angle \( x \)

An interior angle and its corresponding exterior angle are supplementary, meaning they add up to \( 180^{\circ} \). So, \( x=180^{\circ}-I \).
Substitute \( I = 108^{\circ} \):

$$ x = 180^{\circ}- 108^{\circ}=72^{\circ} $$

Answer:

\( x = 72.0 \)