The following diagonal is drawn in a regular heptagon, creating a pentagon and a quadrilateral. What is the measure of $x$, in degrees? Express your answer as a common fraction.

Guest Jun 27, 2018

#1**+2 **

The sum of the interior angles of the heptagon will be (7 - 2) * 180 = 900°

So...each angle will measure (900/7)°

And the sum of the interior angles in the quadrilateral is (4 - 2)* 180 = 360°

So...in the quadrilateral we have that the sum of the angles = 360°

x + x + 2 (900/7) = 360 simplify

2x + 1800/ 7 = 360

2x = 360 - 1800/7

2x = [ 7 * 360 - 1800 ] / 7

2x = [720] / 7 divide both sides by 2

x = [ 720 ] / 14

x = [360 / 7 ]°

CPhill Jun 27, 2018