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 (square or rhombus, but regular, so square). A regular quadrilateral has 4 sides.

Step2: Find the interior angle of a regular quadrilateral

The formula for the interior angle of a regular polygon is $\frac{(n - 2)\times180^{\circ}}{n}$, where $n$ is the number of sides. For $n = 4$, interior angle $=\frac{(4 - 2)\times180^{\circ}}{4}=\frac{2\times180^{\circ}}{4}=90^{\circ}$.

Step3: Find the exterior angle (x)

An interior angle and its corresponding exterior angle are supplementary, so $x + 90^{\circ}=180^{\circ}$. Solving for $x$, we get $x = 180^{\circ}- 90^{\circ}=90^{\circ}$? Wait, no, wait. Wait, a regular quadrilateral (square) has exterior angles? Wait, no, maybe the polygon is a regular quadrilateral, but wait, the diagram looks like a square, but maybe I misidentified. Wait, no, a regular polygon's exterior angle sum is $360^{\circ}$, so for $n$ sides, each exterior angle is $\frac{360^{\circ}}{n}$. For $n = 4$, exterior angle is $\frac{360^{\circ}}{4}=90^{\circ}$. Wait, but that's the same as interior? No, no, interior and exterior are supplementary. Wait, no, in a square, each interior angle is $90^{\circ}$, so exterior angle is also $90^{\circ}$? Wait, no, that can't be. Wait, no, the exterior angle is formed by extending a side. So for a square, if you extend a side, the exterior angle is $90^{\circ}$, because $180 - 90 = 90$. Wait, yes. So for a regular quadrilateral (4 sides), each exterior angle is $\frac{360}{4}=90^{\circ}$. Wait, but maybe the polygon is a regular quadrilateral, so $x$ is the exterior angle. So $x = \frac{360}{4}=90$. Wait, but that seems odd. Wait, maybe the diagram is a regular quadrilateral, so the exterior angle is $90^{\circ}$.

Wait, maybe I made a mistake. Wait, let's recheck. The formula for exterior angle of a regular polygon is $E=\frac{360^{\circ}}{n}$, where $n$ is the number of sides. For $n = 4$, $E = 90^{\circ}$. So $x = 90^{\circ}$.

Answer:

$90$