Question

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:

Step1: Identify the polygon type

The diagram shows a regular quadrilateral (a square or rhombus, but since it's regular, all angles are equal). A regular quadrilateral has 4 sides.

Step2: Use the formula for interior angles of a regular polygon

The formula for the measure of each interior angle of a regular polygon with \( n \) sides is \( \frac{(n - 2)\times180^\circ}{n} \). For \( n = 4 \) (quadrilateral), we substitute:

$$ \frac{(4 - 2)\times180^\circ}{4} = \frac{2\times180^\circ}{4} = \frac{360^\circ}{4} = 90^\circ $$

Answer:

\( 90 \)