Question

A polygon has 7 sides. The interior angle measures are 115, 110, 143, 126, 198, 141, and x. Find the value of x.

Answer 1

Given:

A polygon has 7 sides. The interior angle measures are 115, 110, 143, 126, 198, 141, and x.

Required:

To find the value of x.

Explanation:

The sum of the interior angle in 7 sided polygon is,

$\begin{gathered} =(n-2)\times180\degree \\ \\ =(7-2)\times180\degree \\ \\ =900\degree \end{gathered}$

Therefore,

$\begin{gathered} 115+110+143+126+198+141+x=900 \\ \\ 833+x=900 \\ \\ x=900-833 \\ \\ x=67 \end{gathered}$

Final Answer:

$x=67$