Question

find the angle of depression from point a to point c. angle of depression = ?°

Explanation:

Step1: Use the property of parallel lines and alternate - interior angles

Since the horizontal lines are parallel, the angle of depression from \(A\) to \(C\) is equal to the angle at \(C\) in the right - triangle \(ABC\). Also, in right - triangle \(ABC\), the sum of the two non - right angles is \(90^{\circ}\). Let the angle of depression be \(\theta\).
We know that one of the non - right angles in \(\triangle ABC\) is \(58^{\circ}\), and \(\theta + 58^{\circ}=90^{\circ}\) (because the two non - right angles in a right - triangle are complementary).

Step2: Solve for \(\theta\)

Subtract \(58^{\circ}\) from both sides of the equation \(\theta + 58^{\circ}=90^{\circ}\).
\(\theta=90^{\circ}-58^{\circ}\)

Answer:

\(32\)