The angle sum of all interior angles of a convex polygon of sides 7 is

900°

Exterior angles: \(\frac{360º }{ n}\)

According to the question, n = 7

Exterior angle of the polygon with 7 sides = \(\frac{360º }{ 7}\) 

Interior angle of the polygon with 7 sides = 180º - \(\frac{ 360º}{7 }\) [Sum of all the angles on a straight line = 180º]

= 180º - \(\frac{ 360º}{7 }\)

= \(\frac{ \text{ 1260º - 360º} }{7 }\)

= \(\frac{ \text{ 900º} }{7 }\)

Thus, sum of all the interior angles of the polygon = \(\frac{ \text{ 900º} }{7 }\) x 7 = 900º