A regular hexagon ABCDEF and a square ABGH are formed on opposite side of AB. Find the measure of angle GBC and angle BGC.

Answer 1

since you have one interior angle of regular hexagon (120) and one interior angle of square (90) and Angle GBC forms 360 degree;

this gives us 120 + 90+ GBC=360. solve this to find GBC

we have isosceles triangle then BGC is equal to CGB, lets say BGC =x

so; x+x+GBC =180

I hope that helps