Question

(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.

Answer 1

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':

$\sf 5(x-2)=(x+14)$

Distribute 5 into the parenthesis:

$\sf 5x-10=x+14$

Add 10 to both sides:

$\sf 5x=x+24$

Subtract 'x' to both sides:

$\sf 4x=24$

Divide 4 to both sides:

$\sf x=6$

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

$\sf x+14$

$\sf 6+14$

$\boxed{\sf 20\textdegree}$

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

Answer 2

Answer:

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