Why is the angle exactly 1/2 of one of the angles in the isosceles triangle

I'm sure there's a simple theorem that answers my question, but I'm unsure as to how to formulate the problem (not easy to describe geometry with words): It's a isosceles triangle where you draw a normal line on one of the "hypotenuse" sides, and then you make a right angled triangle out of that. My question is why is the 30 degree angle exactly 1/2 of the 60 degree angles we find in the isosceles triangle?

I'm sure there's a simple theorem that answers my question, but I'm unsure as to how to formulate the problem (not easy to describe geometry with words): It's a isosceles triangle where you draw a normal line on one of the "hypotenuse" sides, and then you make a right angled triangle out of that. My question is why is the 30 degree angle exactly 1/2 of the 60 degree angles we find in the isosceles triangle?