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 = \square^\circ

Explanation:

Step1: Identify the polygon type

The diagram shows a regular quadrilateral (a square or rhombus, but regular, so all sides and angles equal). A regular quadrilateral has 4 sides.

Step2: Recall the formula for exterior angles of a regular polygon

The sum of exterior angles of any polygon is \( 360^\circ \). For a regular polygon with \( n \) sides, each exterior angle \( x \) is given by \( x=\frac{360^\circ}{n} \).

Step3: Calculate the exterior angle

For a quadrilateral, \( n = 4 \). So \( x=\frac{360^\circ}{4}=90^\circ \)? Wait, no, wait. Wait, the diagram: wait, maybe it's a regular quadrilateral? Wait, no, wait, a regular polygon with 4 sides (square) has each interior angle \( 90^\circ \), and exterior angle is \( 180 - 90 = 90 \)? Wait, no, exterior angle is supplementary to interior angle. Wait, no, the formula for exterior angle of regular polygon is \( \frac{360}{n} \). For \( n = 4 \), exterior angle is \( 90^\circ \). Wait, but let's check. Wait, the diagram: the polygon is a regular quadrilateral (4 sides). So \( n = 4 \). Then each exterior angle is \( \frac{360}{4}=90^\circ \). Wait, but maybe I made a mistake. Wait, no, the formula for exterior angles: sum of exterior angles of any convex polygon is \( 360^\circ \). So for regular polygon, each exterior angle is \( \frac{360}{n} \). So for \( n = 4 \), \( 360/4 = 90 \). So \( x = 90 \). Wait, but let's confirm. The interior angle of a regular quadrilateral is \( (4 - 2)\times180/4 = 90^\circ \), so exterior angle is \( 180 - 90 = 90^\circ \). Yes, that matches. So \( x = 90 \).

Wait, but maybe the polygon is a regular quadrilateral (square), so exterior angle is 90 degrees. So the calculation is correct.

Answer:

\( 90 \)