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°. find the value of x
135°
90°
30°
45°

Explanation:

Step1: Set up the equation

The sum of the interior angles of the pentagon is \(540^{\circ}\). The angles are \(2x\), \(3x\), \(2x\), \(2x\), \(3x\). So, \(2x + 3x+2x + 2x+3x=540\).

Step2: Simplify the left - hand side

Combine like terms: \((2 + 3+2 + 2+3)x=12x\). So the equation becomes \(12x = 540\).

Step3: Solve for \(x\)

Divide both sides of the equation by \(12\): \(x=\frac{540}{12}=45\).

Answer:

\(45^{\circ}\)