Question

1. find the measure of x. 117° 100° 105° 115° x° 105° 117° 103° 110°

Explanation:

Step1: Recall polygon - angle sum formula

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

Step2: Set up an equation

Let the unknown angle be $x$. We have the equation $117^{\circ}+100^{\circ}+105^{\circ}+115^{\circ}+x = 540^{\circ}$.

Step3: Simplify the left - hand side

$117 + 100+105 + 115=437$. So the equation becomes $437^{\circ}+x = 540^{\circ}$.

Step4: Solve for $x$

Subtract $437^{\circ}$ from both sides: $x=540^{\circ}-437^{\circ}=103^{\circ}$.

Answer:

$103^{\circ}$