Question

the polygon has 7 sides.
what is the value of x?
image of a heptagon with angles: 115°, 145°, 140°, x°, 128°, 130°, 120°

Explanation:

Step1: Calculate the sum of interior angles

The formula for the sum of interior angles of an \(n -\)sided polygon is \((n - 2)\times180^{\circ}\). For \(n = 7\), \((7-2)\times180^{\circ}=900^{\circ}\)

Step2: Set up an equation to find \(x\)

Sum of given angles: \(120 + 130+128 + 115+145+140+x\)
\(120+130 + 128+115+145+140+x=900\)
\((120+130)+(128+115)+(145+140)+x=900\)
\(250+243+285+x=900\)
\(778+x=900\)
\(x=900 - 778\)

Answer:

\(x = 122^{\circ}\)