Question

in each diagram find the value of x. remember -> sum of interior angles=(n - 2)·180

Explanation:

Step1: Identify polygon and find sum of interior angles for left - hand problem

The polygon on the left has 4 sides ($n = 4$). Using the formula $(n - 2)\times180$, we get $(4 - 2)\times180=360^{\circ}$.

Step2: Set up equation for left - hand problem

The sum of the interior angles of the 4 - sided polygon is $60 + x+80 + 90=360$.

Step3: Solve for $x$ in left - hand problem

Combining like terms gives $x+230 = 360$. Then $x=360 - 230=130$.

Step4: Identify polygon and find sum of interior angles for right - hand problem

The polygon on the right has 5 sides ($n = 5$). Using the formula $(n - 2)\times180$, we get $(5 - 2)\times180 = 540^{\circ}$.

Step5: Set up equation for right - hand problem

The sum of the interior angles of the 5 - sided polygon is $110+100+x + 80+120=540$.

Step6: Solve for $x$ in right - hand problem

Combining like terms gives $x + 410=540$. Then $x=540 - 410 = 130$.

Answer:

Problem on Left: $x = 130$
Problem on Right: $x = 130$