four interior angles of a pentagon measure $88^\\circ$, $118^\\circ$, $132^\\circ$, and $100^\\circ$. what…

four interior angles of a pentagon measure $88^\\circ$, $118^\\circ$, $132^\\circ$, and $100^\\circ$. what is the measure of the fifth interior angle?\n$82^\\circ$\n$92^\\circ$\n$102^\\circ$\n$112^\\circ$

four interior angles of a pentagon measure $88^\\circ$, $118^\\circ$, $132^\\circ$, and $100^\\circ$. what is the measure of the fifth interior angle?\n$82^\\circ$\n$92^\\circ$\n$102^\\circ$\n$112^\\circ$

Answer

Explanation:

Step1: Find total interior angle sum

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

Step2: Sum given four angles

Add the provided angle measures: $$88^\circ + 118^\circ + 132^\circ + 100^\circ = 438^\circ$$

Step3: Calculate fifth interior angle

Subtract the sum of the four angles from the total interior angle sum: $$540^\circ - 438^\circ = 102^\circ$$

Answer:

C. 102°