Question

given that parallel lines ( k ) and ( j ) are cut by transversal ( l ) and ( angle 1 = 140^{circ} ), find the measure of: angle 5 a. ( 140^{circ} ) b. ( 40^{circ} ) c. ( 50^{circ} ) d. ( 60^{circ} )

Explanation:

Step1: Find the measure of ∠4

Since ∠1 and ∠4 are supplementary angles (they form a linear pair), we know that ∠1 + ∠4 = 180°. Given ∠1 = 140°, then ∠4 = 180° - 140° = 40°.

Step2: Use the property of parallel lines and transversal

When two parallel lines \(k\) and \(j\) are cut by a transversal \(l\), ∠4 and ∠5 are alternate interior angles. Alternate interior angles are congruent. So ∠5 = ∠4.

Answer:

B. \(40^{\circ}\)