Question

angles of polygons scavenger hunt find the value of x in the figure below: (9x)°

Explanation:

Step1: Identify the polygon type

The figure is a regular octagon (all sides equal, so all interior angles equal). For a regular polygon with \( n \) sides, the formula for each interior angle is \( \frac{(n - 2)\times180^\circ}{n} \). For an octagon, \( n = 8 \).

Step2: Calculate the interior angle

Substitute \( n = 8 \) into the formula:
\( \frac{(8 - 2)\times180^\circ}{8}=\frac{6\times180^\circ}{8}=\frac{1080^\circ}{8} = 135^\circ \).
But the angle is given as \( 9x^\circ \), so set \( 9x = 135 \).

Step3: Solve for \( x \)

Divide both sides by 9:
\( x=\frac{135}{9}=15 \).

Answer:

\( x = 15 \)