The measure of the angle of elevation from point A to point B. is (3x+1)^{\circ} The measure of D, the angle of depression from point B to point A. is 2(x+8)^{\circ} Find the measure of each angle.

(1 point)

m\angle B=22^{\circ} m\angle D=30^{\circ}

m\angle B=15 m\angle D=15^{\circ}

m\angle B=46^{\circ} m\angle D=46^{\circ}

m\angle B=52^{\prime},m\angle D=50^{\circ}

1 answer

The measure of the angle of elevation from point A to point B is (3x+1)°.
The measure of the angle of depression from point B to point A is 2(x+8)°.

To find the value of x, we set the two angles equal to each other:
(3x+1)° = 2(x+8)°

Simplifying the equation:
3x + 1 = 2x + 16
x = 15

Now that we know the value of x, we can find the measure of each angle:
Angle B = (3x+1)° = (3*15+1)° = 46°
Angle D = 2(x+8)° = 2(15+8)° = 46°

Therefore, the measure of angle B is 46° and the measure of angle D is also 46°.