Question

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

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 six angles is \(776^{\circ}\). Using the equation \(S=\text{sum of six angles}+x\), we substitute \(S = 900^{\circ}\) and the sum of six angles \(=776^{\circ}\). Then \(x=900^{\circ}-776^{\circ}\).

Answer:

\(124^{\circ}\)