the diagram shows a regular polygon.\nwhat is the value of x?\nwrite your answer as an integer or as a…

the diagram shows a regular polygon.\nwhat is the value of x?\nwrite your answer as an integer or as a decimal rounded to the nearest tenth.\n$x = \\square^\\circ$

the diagram shows a regular polygon.\nwhat is the value of x?\nwrite your answer as an integer or as a decimal rounded to the nearest tenth.\n$x = \\square^\\circ$

Answer

Explanation:

Step1: Identify the number of sides

The polygon shown is a regular octagon, so the number of sides ( n = 8 ).

Step2: Find the measure of an interior angle

The formula for the measure of an interior angle of a regular polygon is ( \frac{(n - 2)\times180^\circ}{n} ). Substituting ( n = 8 ): [ \frac{(8 - 2)\times180^\circ}{8}=\frac{6\times180^\circ}{8}=\frac{1080^\circ}{8} = 135^\circ ]

Step3: Find the value of ( x )

The angle ( x ) and the interior angle are supplementary (they form a linear pair), so ( x = 180^\circ - 135^\circ ). [ x = 45^\circ ]

Answer:

( 45.0 ) (or ( 45 ))