For the considered regular polygon with number of sides as five, the value of x in the expression for one of its internal angle is 14
What is the sum of all the exterior angles of a regular polygon?
For a regular polygon of any number of sides, the sum of its exterior angle is 360° (full angle).
Exterior angle is an measure of rotation between one extended side(we extend it virtually) of the polygon with its adjacent side which is not extended.
Also, due to polygon being regular, let it be having 'n' sides, all the exterior angles are of same measure, and therefore, their measure is (360/n)°.
For this case, consider the diagram attached below.
The measure of the angle OAD is 180° because of it forming straight line.
Also, each of the exterior angle of this regular pentagon is
(360/5)° = 72°.
Thus, we have:
[tex]\angle BAD = 72^\circ\\\angle OAB = (9x - 18)^\circ\\\angle OAD = \angle OAB + \angle BAD = 180^\circ\\\\9x - 18 + 72 = 180\\\\9x + 54 = 180\\\\x = \dfrac{180 - 54}{9} = \dfrac{126}{9} = 14[/tex]
Thus, for the considered regular polygon with number of sides as five, the value of x in the expression for one of its internal angle is 14
Learn more about interior and exterior angles of a regular polygon here:
https://brainly.com/question/14173422
