Question

four interior angles of a pentagon measure 156°, 72°, 98°, and 87°. what is the measure of the final interior angle? 108° 127° 150° 487°

Explanation:

Step1: Calculate the sum of interior angles of a pentagon

The formula for the sum of interior angles of a polygon is \((n - 2)\times180^{\circ}\), where \(n\) is the number of sides. For a pentagon, \(n = 5\), so the sum is \((5 - 2)\times180^{\circ}=540^{\circ}\).

Step2: Find the measure of the unknown angle

Let the unknown angle be \(x\). We know that \(156^{\circ}+72^{\circ}+98^{\circ}+87^{\circ}+x = 540^{\circ}\). First, calculate the sum of the known angles: \(156 + 72+98 + 87=413\). Then, \(x=540 - 413 = 127^{\circ}\).

Answer:

\(127^{\circ}\) (the second option)