For a end project in a math class, I am going to attempt to figure out the laws for spherical trigonometry. Specificially, side lengths and areas for triangles on a sphere. I am fairly sure I know how to go about side lengths, and I have an idea how to go about the area of a curved triangle, but it's dependent on an assumption I want to make sure is correct. Without going into details, the assumption is that increasing the interior angle sum (past 180 degrees) will increase the area by an amount dependent only on the angle increase (and the dimensions of the triangle), meaning it doesn't matter which angle is being increased, just that the total angle is being increased. Is this correct? I would appreciate non specifics if it is wrong- I want to try to figure it out by my self. Thank you.