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A nonregular hexagon has five exterior angle measures of 55, 58, 69, 57 and 55. What is the measure of the interior angle adjacent to the sixth exterior angle?

Respuesta :

bcalle
The exterior angles will have a sum of 360. First find the missing exterior angle.
360-(55+ 58+ 69+ 57+ 55)
360-(294)=66
The interior and exterior angles are supplementary so the interior angle is 180-66
= 114

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 [tex]114\textdegree[/tex].

Given:  Non regular hexagon whose five exterior angles be  

            [tex]\rm 55 \textdegree,58\textdegree,69\textdegree,57\textdegree\& \;55\textdegree[/tex]

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 = [tex]360\textdegree[/tex] now let the sixth angle be x

To find the value of x we will simplify,

[tex]\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[/tex]

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.

[tex]\rm Interior \;\;angle + 66\textdegree = 180\textdegree\\Interior\; angle = 180\textdegree - 66\textdegree = 114\textdegree[/tex]

Therefore, The measure of the interior angle is 114°

Learn more about Exterior and Interior angle here : https://brainly.com/question/14281338