Question

the sum of the interior angles of a hendecagon is greater than...
two of these.
the sum of the interior angles of a 15 - gon.
the sum of the interior angles of a nonagon.
the sum of the exterior angles of a decagon.

Explanation:

Step1: Recall the formula for sum of interior angles

The formula for the sum of interior angles of an \(n -\)sided polygon is \(S=(n - 2)\times180^{\circ}\).

Step2: Calculate sum of interior angles of hendecagon

A hendecagon has \(n = 11\) sides. So \(S_{11}=(11 - 2)\times180^{\circ}=9\times180^{\circ}=1620^{\circ}\).

Step3: Calculate sum of interior angles of 15 - gon

For a 15 - gon with \(n = 15\), \(S_{15}=(15 - 2)\times180^{\circ}=13\times180^{\circ}=2340^{\circ}\). Since \(1620^{\circ}<2340^{\circ}\), the sum of interior angles of a hendecagon is less than that of a 15 - gon.

Step4: Calculate sum of interior angles of nonagon

For a nonagon with \(n = 9\), \(S_{9}=(9 - 2)\times180^{\circ}=7\times180^{\circ}=1260^{\circ}\). Since \(1620^{\circ}>1260^{\circ}\), the sum of interior angles of a hendecagon is greater than that of a nonagon.

Step5: Recall sum of exterior angles of any polygon

The sum of exterior angles of any polygon is \(360^{\circ}\). For a decagon, the sum of exterior angles is \(360^{\circ}\), and \(1620^{\circ}>360^{\circ}\). But we are looking for a single - correct answer among the non - "two of these" options, and the most straightforward comparison among single polygon angle - sum cases is with the nonagon.

Answer:

C. the sum of the interior angles of a nonagon.