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°.
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.
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