The measure of ∠E, the angle of elevation from point A to point B, is (3x + 1)°. The measure of ∠D, the angle of depression from point B to point A is 2(x + 8)°. Find the measure of each angle.

1 answer

We know that the angle of elevation (∠E) from point A to point B and the angle of depression (∠D) from point B to point A are alternate angles. Alternate angles are equal when a line intersecting two parallel lines is intersected by a transversal. Therefore, we can set the two expressions equal to each other and solve for x.

3x + 1 = 2(x + 8)

3x + 1 = 2x + 16

x = 15

Now that we know x, we can substitute it into the expressions for the angles of elevation and depression to find their measures:

∠E = 3(15) + 1 = 46°

∠D = 2(15 + 8) = 46°

Therefore, the measure of the angle of elevation (∠E) is 46°, and the measure of the angle of depression (∠D) is also 46°.