From the figure above In △BOC, 2x + 30º = 180º Therefore, x = \(\frac{180º - 30º}{2}\) = 75º Each interior angle = 2 times x = 2 x 75 = 150º OR To calculate the interior angle of a regular convex polygon where each side subtends an angle of \(30^\circ\) at the center, we follow these steps: Determine the number of sides (n) The angle subtended at the center by each side is given as \(30^\circ\). The total angle around a point is \(360^\circ\). \(n = \frac{360^\circ}{30^\circ}\) = 12 So, the polygon has 12 sides. Calculate the interior angle. The formula for the interior angle A of a regular polygon is: \(A = \frac{(n - 2) \times 180^\circ}{n}\) Substituting n = 12: \(A = \frac{(12 - 2) \times 180^\circ}{12} = \frac{10 \times 180^\circ}{12} = \frac{1800^\circ}{12} = 150^\circ\) Each interior angle of the regular convex polygon is \(150^\circ\).