four interior angles of a pentagon measure 88°, 118°, 132°, and 100°. what is the measure of the fifth…

Explanation:

Step1: Recall sum - of - interior - angles formula

The sum of interior angles of an $n$-sided polygon is given by $(n - 2)\times180^{\circ}$. For a pentagon, $n = 5$, so the sum of interior angles is $(5 - 2)\times180^{\circ}=3\times180^{\circ}=540^{\circ}$.

Step2: Calculate the sum of the four given angles

$88^{\circ}+118^{\circ}+132^{\circ}+100^{\circ}=(88 + 118)+(132 + 100)=206^{\circ}+232^{\circ}=438^{\circ}$.

Step3: Find the fifth angle

Let the fifth angle be $x$. Then $x=540^{\circ}-438^{\circ}=102^{\circ}$.

Answer:

$102^{\circ}$