Chapter 4.6, Problem 49MS

Here we celebrate the power of algebra as a powerful way of finding unknown quantities by naming them, of expressing infinitely many relationships and connections clearly and succinctly, and of uncovering pattern and structure.

Negative x? A triangle is drawn on a surface having negative curvature. Two of the angles measure 80 degrees. If x is the measure of the third angle, and x satisfies the equation $x^2-25x+100=0,findx.$

(There’s only one value for x that works. What is it and why ?)