Question

an irregular pentagon is constructed such that the measures of all interior angles are unique integers which share a greatest common divisor greater than 1. suppose that the measure of the smallest interior angle is found to be 55°. what is the sum of the measures of the other 4 interior angles?

665°
485°
535°
305°
125°

Explanation:

Step1: Recall sum of interior angles of pentagon

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

Step2: Calculate sum of other 4 angles

Let the sum of the other 4 interior - angles be $x$. We know that one angle is $55^{\circ}$. So, $x+55^{\circ}=540^{\circ}$. Then $x = 540^{\circ}-55^{\circ}=485^{\circ}$.

Answer:

$485^{\circ}$