(60 POINTS)The measure of angle E, the angle of elevation from point A to point B, is 5(x-2) degrees. The measure of D, the angle of depression from point B to point A is (x + 14) degrees. Find the measure of each angle.

Take a look at the figures, it's the same angle from a different point of view, so since they are both equal we can set these two equations equal to each other, then solve for 'x':

[tex]\sf 5(x-2)=(x+14)[/tex]

Distribute 5 into the parenthesis:

[tex]\sf 5x-10=x+14[/tex]

Add 10 to both sides:

[tex]\sf 5x=x+24[/tex]

Subtract 'x' to both sides:

[tex]\sf 4x=24[/tex]

Divide 4 to both sides:

[tex]\sf x=6[/tex]

So this is our value of 'x', we can plug it into any of the two equations to find the measurement for both angles:

[tex]\sf x+14[/tex]

[tex]\sf 6+14[/tex]

[tex]\boxed{\sf 20\textdegree}[/tex]

So the length of both angle E and angle D is 20 degrees.