In the figure, lines m and n are parallel and are cut by a transversal. If ∠1 = (4x + 5)° and ∠2 = (6x − 15)°, find x.
Explanation
📌 Step 1: Identify the angle relationship
∠1 and ∠2 are in the same position relative to the transversal at each parallel line → corresponding angles.
📌 Step 2: Apply the theorem
Corresponding angles are equal when lines are parallel:
4x + 5 = 6x − 15
📌 Step 3: Solve
5 + 15 = 6x − 4x
20 = 2x
x = 10
📌 Verify: ∠1 = 4(10)+5 = 45° and ∠2 = 6(10)−15 = 45° ✓
💡 Tip: If the angles are in the SAME position at each intersection → corresponding → equal.