Question

type the correct answer in the box. find the value of x in the figure. (4x - 5)° 117° (4x - 3)° (3x - 3)° 118° (3x + 6)° x=

Explanation:

Step1: Recall sum - of - interior - angles formula

The sum of the interior angles of an $n$-sided polygon is given by $(n - 2)\times180^{\circ}$. Here, $n = 6$, so the sum is $(6 - 2)\times180^{\circ}=720^{\circ}$.

Step2: Set up an equation

Add up all the angle measures in the hexagon: $(4x - 5)+(4x - 3)+117+(3x - 3)+118+(3x + 6)=720$.

Step3: Combine like - terms

$(4x+4x + 3x+3x)+(-5-3 + 117-3 + 118+6)=720$.
$14x+( - 8+117-3 + 118+6)=720$.
$14x+(109-3 + 118+6)=720$.
$14x+(106+118+6)=720$.
$14x+(224+6)=720$.
$14x + 230=720$.

Step4: Solve for $x$

Subtract 230 from both sides: $14x=720 - 230$.
$14x=490$.
Divide both sides by 14: $x=\frac{490}{14}=35$.

Answer:

$35$