The following diagonal is drawn in a regular heptagon, creating a pentagon and a quadrilateral.
Another diagonal is drawn.
What is the measure of x, in degrees? Express your answer as a common fraction.
If the heptagon were inscribed in a circle, each side of of the heptagon would span an arc of ( 360 / 7)°
The diagonals would form chords within this circle
So....using the angle of intersecting chords theorem we have that
x = (1/2) [ 2 (360/7) + 3(360/7) ] = (1/2) [ 5 (360/7 ] = [900/7]° ( ≈ 128.57° )