You need this key result: in any polygon, the sum of the interior angles is
where
is the number of sides of the polygon.
Your polygon has seven sides, and the measures of all angles are given. So, we can write
Again, we've simply written that the sum of all interior angles is the number of sides, minus two, times 180.
We can simplify both sides: we sum like terms on the left hand side, and we easily compute the right hand side:
and we can solve this equation for
by dividing both sides by 30:
Finally, the required angles is
