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 quadrilateral (a rhombus, which is also a type of regular polygon with 4 sides). For a regular polygon with \( n \) sides, the formula for the measure of each interior angle is \( \frac{(n - 2)\times180^\circ}{n} \). Here, \( n = 4 \) (since it's a quadrilateral).

Step2: Calculate the interior angle

Substitute \( n = 4 \) into the formula:
\[
\frac{(4 - 2)\times180^\circ}{4} = \frac{2\times180^\circ}{4} = \frac{360^\circ}{4} = 90^\circ
\]

Answer:

\( x = 90 \)