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 (\(n=7\)), we have \((7 - 2)\times180^{\circ}=5\times180^{\circ}=900^{\circ}\).

Step2: Find the measure of the unknown interior angle

Let the unknown interior angle be \(x\). We know that the sum of six interior angles is \(776^{\circ}\). Using the equation \(x+776^{\circ}=(7 - 2)\times180^{\circ}\), we substitute the sum of interior angles of the heptagon. Then \(x = 900^{\circ}-776^{\circ}\).

Answer:

\(124^{\circ}\)