Question

What are the measures of the exterior angles of the polygon shown? 1. (x + 15)° 2. (4x - 10)° 3. (3x + 10)° 4. (2x + 5)° 5. 3x°

Answer 1

At first for any polygon the sum of the exterior angles = 360

For the given polygon, we need to find the measures of the exterior angles

We will find the value of x, then we will evaluate the exterior angles

The given polygon has 5 sides , so, the sum of the interior angles = (n - 2) * 180

`=(5-2)\cdot180=540`

So, the sum of the angles is :

`(x+15)+(4x-10)+(3x+10)+(2x+5)+3x=540`

Solve the equation for x:

`\begin{gathered} 13x+20=540 \\ 13x=540-20 \\ 13x=520 \\ \\ x=(520)/(13)=40 \end{gathered}`

So, the measures of the angles will be as following :

`\begin{gathered} \angle1=180-(x+15)=180-(40+15)=125 \\ \\ \angle2=180-(4x-10)=180-(4\cdot40-10)=180-150=30 \\ \\ \angle3=180-(3x+10)=180-(3\cdot40+10)=180-130=50 \\ \\ \angle4=180-(2x+5)=180-(2\cdot40+5)=180-85=95 \\ \\ \angle5=180-3x=180-3\cdot40=180-120=60 \end{gathered}`