Question

The measure of Angle E, the angle of elevation from point A to point B, is 5 left-parenthesis x minus 2 right parenthesis-degrees. The measure of Angle D, the angle of depression from point B to point A, is left-parenthesis x plus 14 right parenthesis-degrees. Find the measure of each angle.

Answer 1

measure of angle E equals 20 degrees, measure of angle D equals 20 degrees

Answer 2

We have that those 2 angles have to be equal because the line that connects the 2 points has the same angle to any horizontal line that cuts it. Hence,
5(x-2)=x+14. This is a standard first-degree equation that can be solved by splitting knowns and unknowns.
5x-10=x+14. 4x=24. x=6. Substituting in one of the two equivalent expressions, angle=x+14=20 degrees.