If you make 7 triangles by joining each vertex to the centre, the angles at the centre must add up to 360°.
In a regular heptagon each central angle would be 360/7 degrees, and the other two peripheral angles in the triangle are the same, because each triangle is isosceles. So each of the other angles would be (180-360/7)/2=90-180/7.
Two adjacent outer angles of the triangle make an interior angle=180-360/7 degrees and since there are 7 of these, the total of all the interior angles is 7(180-360/7)=1260-360=900°. This angle sum is the same for all heptagons, so the sum of the remaining angles=900-(109+158+117+98)=900-482=418°.