Correct Answer: Option B

Explanation

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 \(150^\circ\).

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