Final Answer:
Given that line ab is parallel to ef and transversal gj intersects ab at point k and ef at point l, with angle elj measuring 120 degrees, Daniel can show that m∠gkb = 120° by applying the alternate interior angles theorem. Since ab is parallel to ef, angle elj = angle gkb due to alternate interior angles, therefore m∠gkb = 120°.
Step-by-step explanation:
The alternate interior angles theorem states that when two parallel lines are intersected by a transversal, the pairs of alternate interior angles are congruent. In this scenario, line ab is parallel to ef, and transversal gj intersects them at points k and l. Angle elj measures 120 degrees, and as line ab is parallel to ef, angle elj corresponds to angle gkb due to alternate interior angles. Therefore, m∠gkb = 120° by the alternate interior angles theorem.
The given information of parallel lines ab and ef intersected by transversal gj at points k and l allows for the identification of angle measures based on the properties of parallel lines and transversals. In this case, the measurement of angle elj, being 120 degrees, directly corresponds to angle gkb due to the theorem governing the relationships between alternate interior angles when parallel lines are crossed by a transversal. Hence, Daniel can confidently assert that the measure of angle gkb is also 120 degrees based on the alternate interior angles theorem in the context of parallel lines and transversals.
This proof demonstrates the application of geometric principles involving parallel lines and transversals to establish the equality of angle measures. Utilizing the alternate interior angles theorem, Daniel can assert that angle gkb measures 120 degrees by drawing a clear relationship between the given angle elj and the corresponding angle gkb due to the properties of intersecting parallel lines by a transversal.