Question

find the sum of the interior angles of the following polygon: polygon image with angles 115°, 95°, 115°, 130°, x sum of interior angles = degrees. part 2: find the measure of x: x = degrees.

Explanation:

Step1: Use the formula for sum of interior angles

The formula for the sum of interior angles of an \(n -\)sided polygon is \((n - 2)\times180^{\circ}\). Here, \(n=6\) (the polygon has 6 sides).

$$S=(6 - 2)\times180^{\circ}=4\times180^{\circ}=720^{\circ}$$

Step2: Find the value of \(x\)

We know that the sum of all interior angles is \(720^{\circ}\). So, \(x+115^{\circ}+95^{\circ}+115^{\circ}+130^{\circ}+ \text{another angle}\). Wait, no, wait, the sum of angles \(x + 115+95 + 115+130+ \text{missing angle}\). Wait, no, using the sum formula result.
We have \(x+115 + 95+115+130+115=720\) (since sum \(S = 720\)).

$$x+(115\times3)+130 + 95=720$$

$$x + 345+130+95=720$$

$$x+570=720$$

$$x=720 - 570$$

$$x = 150^{\circ}$$

Answer:

Sum of interior angles \(= 720\) degrees.
\(x = 150\) degrees.