Question

The convex polygon below has 8 sides. Find the value of x.140°11801270153013401561170

Answer 1

`x=135`

Step-by-step explanation

The formula for calculating the sum of interior angles in a polygon is ( n − 2 ) × 180 ∘ where is the number of sides.

`(n-2)\cdot180=\text{ Sum of internal angles}`

Step 1

find the sum of the internal angles in the given polygon

Let

number of sides = 8

Now, replace

`\begin{gathered} (n-2)\cdot180=\text{ Sum of internal angles} \\ (8-2)\cdot180=\text{ Sum of internal angles} \\ 6\cdot180=\text{Sum of internal angles} \\ 1080=\text{Sum of internal angles}\rightarrow equation(1) \end{gathered}`

Step 2

now, we have the other angles, so

sum of internal angles is:

`\text{angle}1+\text{angle}2+\text{angle}3+\text{angle}4+\text{angle}5+\text{angle}6+\text{angle}7+\text{angle}8=\text{ sum of the internal angles}`

replace

`\begin{gathered} 127+140+118+153+156+117+x+132=\text{ Sum of internal angles} \\ x+943=\text{Sum of internal angles}\rightarrow equation\text{ (2)} \end{gathered}`

hence

`x+945=1080`

subtract 945 in both sides to solve for x

`\begin{gathered} x+945=1080 \\ x+945-945=1080-945 \\ x=135 \end{gathered}`

i hope this helps you