Question

the measure of angle e, the angle of elevation from point a to point b, is (3x+1). The measure of angle s, the angle of depression from point b to point a, is 2(x+8). Find the measure of each angle.

Answer 1

c    m angle E= 46 degrees,  m angle D=46 degrees

Answer 2

Answer: m∠ E = 46°, m∠ S = 46°

Explanation:

Angle of elevation from point a to b ( angle E ) is the angle between the horizontal and the line from a to b .

And, Angle of depression from b to a ( angle S ) is the angle from the horizontal downward from b to a,

Since, all the horizontal lines are parallel to each other,

By the alternative interior angle theorem,

Angle of elevation from point a to b = Angle of depression from point b to a,

⇒ m ∠ E = m ∠ S

⇒ 3x + 1 = 2(x+8) ( Given )

⇒ 3x + 1 = 2x + 16

⇒ x = 15,

Hence, m∠ E = 3x + 1 = 45 + 1 = 46°

⇒ m∠S = 46°