Question

a recent tornado damaged jacks house and left it a little distorted. a question on the insurance form asked, what shape is the house in? jack replied, an irregular convex pentagon.
the sum of the measures of the interior angles of the 5 - sided house is ( 540^{circ} ). find the value of ( y ).

Explanation:

Step1: Set up the equation

The sum of the interior angles of the pentagon is \(540^{\circ}\). So, \(y+(2y - 6)+(2y+2)+(2y)+(2y + 4)=540\).

Step2: Combine like terms

Combine the \(y\) - terms and the constant terms: \((1 + 2+2+2+2)y+(-6 + 2+4)=540\), which simplifies to \(9y+0 = 540\).

Step3: Solve for \(y\)

Divide both sides of the equation \(9y=540\) by \(9\). So, \(y=\frac{540}{9}\).

Answer:

\(60^{\circ}\)

(It seems there might be a typo in the provided options as the correct value of \(y\) is \(60^{\circ}\) based on the above calculation. If we assume the problem was intended to have a different setup and follow the steps with the given options in mind, perhaps there was an error in transcribing the angle expressions. But following the standard algebraic approach for combining the angle expressions as presented in the problem - setup, the result is \(y = 60^{\circ}\))