four interior angles of a pentagon measure 156°, 72°, 98°, and 87°. what is the measure of the final…

Explanation:

Step1: Find 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). [ \begin{align*} S&=(5 - 2)\times180^{\circ}\ &=3\times180^{\circ}\ &=540^{\circ} \end{align*} ]

Step2: Calculate the sum of the four given angles

[ \begin{align*} 156^{\circ}+72^{\circ}+98^{\circ}+87^{\circ}&=(156 + 72)+(98+87)\ &=228^{\circ}+185^{\circ}\ &=413^{\circ} \end{align*} ]

Step3: Find the measure of the fifth angle

Let the fifth angle be (x). Then (x=540^{\circ}-413^{\circ}) [ x = 127^{\circ} ]

Answer:

B. (127^{\circ})