A nonregular hexagon has five exterior angle measures of 55, 58, 69, 57 and 55 ,the measure of the interior angle adjacent to the sixth exterior angle is \(114\textdegree\).
Given: Non regular hexagon whose five exterior angles be
\(\rm 55 \textdegree,58\textdegree,69\textdegree,57\textdegree\& \;55\textdegree\)
What is non regular hexagon?
Non regular hexagon is where all the angles is not equal.
We know that the Sum of all exterior angle = \(360\textdegree\) now let the sixth angle be x
To find the value of x we will simplify,
\(\rm 55\textdegree + 58\textdegree + 69\textdegree + 57\textdegree+ 55\textdegree + x = 360\textdegree\\294\textdegree + x= 360\textdegreex = 360\textdegree - 294\textdegree\\x = 66\textdegree\)
Here, the measure of the interior angle is adjacent to the sixth exterior angle so,
Interior angle is the difference of 180° to the 6th exterior angle.
\(\rm Interior \;\;angle + 66\textdegree = 180\textdegree\\Interior\; angle = 180\textdegree - 66\textdegree = 114\textdegree\)
Therefore, The measure of the interior angle is 114°
Learn more about Exterior and Interior angle here : https://brainly.com/question/14281338
