Question

the sum of all but one interior angle of a heptagon is 776°. what is the measure of the final interior angle? 42° 56° 124° 304°

Explanation:

Step1: Calculate the sum of interior angles of a heptagon

The formula for the sum of interior angles of an \(n -\)sided polygon is \((n - 2)\times180^{\circ}\). For a heptagon (\(n=7\)), the sum \(S=(7 - 2)\times180^{\circ}=900^{\circ}\)

Step2: Find the measure of the unknown interior angle

Let the unknown angle be \(x\). We know that the sum of all but one interior angle is \(776^{\circ}\). So \(x=S - 776^{\circ}\). Substitute \(S = 900^{\circ}\) into the equation: \(x=900^{\circ}-776^{\circ}=124^{\circ}\)

Answer:

\(124^{\circ}\) (corresponding to the third option)