Question

two parallel lines are cut by a transversal as shown below.

suppose (m \angle 3 = 83^{\circ}). find (m \angle 5) and (m \angle 8).

(m \angle 5 = \square^{\circ})
(m \angle 8 = \square^{\circ})

Explanation:

⚡ Using what you learned: lines and angles (parallel, transversal, vertical)

Step 1: Find \( m\angle 5 \)

Since the two vertical lines are parallel and cut by a transversal, \( \angle 3 \) and \( \angle 5 \) are consecutive interior angles (also known as same-side interior angles). Therefore, they are supplementary:

$$ m\angle 3 + m\angle 5 = 180^\circ $$

$$ 83^\circ + m\angle 5 = 180^\circ $$

$$ m\angle 5 = 180^\circ - 83^\circ = 97^\circ $$

Step 2: Find \( m\angle 8 \)

The angles \( \angle 3 \) and \( \angle 8 \) are alternate exterior angles, which means they are equal:

$$ m\angle 8 = m\angle 3 = 83^\circ $$

Answer:

$$ m\angle 5 = 97^\circ $$

$$ m\angle 8 = 83^\circ $$