Question

two parallel lines are cut by a transversal as shown below.
suppose \\(m \angle 6 = 106^{\circ}\\). find \\(m \angle 1\\) and \\(m \angle 4\\).

Explanation:

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

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

Since the two vertical lines are parallel, corresponding angles are equal.

$$ m\angle 1 = m\angle 5 $$

Angles \( \angle 5 \) and \( \angle 6 \) form a linear pair along the transversal line:

$$ m\angle 5 + m\angle 6 = 180^\circ $$

$$ m\angle 5 + 106^\circ = 180^\circ $$

$$ m\angle 5 = 74^\circ $$

Therefore:

$$ m\angle 1 = 74^\circ $$

Step 2: Find \( m\angle 4 \)

Angles \( \angle 1 \) and \( \angle 4 \) form a linear pair along the left parallel line:

$$ m\angle 1 + m\angle 4 = 180^\circ $$

$$ 74^\circ + m\angle 4 = 180^\circ $$

$$ m\angle 4 = 106^\circ $$

Answer:

$$ m\angle 1 = 74^\circ $$

$$ m\angle 4 = 106^\circ $$