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

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

Answer 2

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.