Question

the angle measures of a polygon with n sides can be found using an equation to find each value of x. justify the steps in your solution. this figure has a sides so the sum of angles is given by s = 180(3 - 2)= n = 3 s = 180×1 = 180 30+(30 + x)+9x = 180 60+10x = 180 10x = 180 - 60 = 120 x = 12

Explanation:

Step1: Apply polygon - angle sum formula

The sum of interior angles of a polygon is $S = 180(n - 2)$. Here $n = 3$, so $S=180\times(3 - 2)=180$.

Step2: Set up equation based on angle measures

The angles of the triangle are $30$, $30 + x$, and $9x$. Their sum is $30+(30 + x)+9x=180$.

Step3: Simplify the left - hand side of the equation

Combine like terms: $30+30 + x+9x=60 + 10x$. So the equation becomes $60+10x = 180$.

Step4: Isolate the term with $x$

Subtract 60 from both sides: $10x=180 - 60=120$.

Step5: Solve for $x$

Divide both sides by 10: $x=\frac{120}{10}=12$.

Answer:

$x = 12$