Question

Line ab is parallel to ef. Transversal gj crosses line ab at k and crosses line ef at l. The measure of angle elj is 120 degrees. Daniel is constructing a fence that consists of parallel sides line ab and line ef. Complete the proof to explain how he can show that m∠gkb = 120° by filling in the missing justifications.

Answer 1

To prove that m∠gkb = 120°, we can use the properties of parallel lines and transversals.

Step-by-step explanation:

In order to show that m∠GKB = 120°, we can use the fact that line AB is parallel to line EF. Since line GJ is a transversal that crosses AB at point K and EF at point L, we can use the properties of parallel lines and transversals to find the measure of angle ELJ.

Since line AB is parallel to line EF, the alternate interior angles ELJ and GKB are congruent. If angle ELJ is 120°, then angle GKB is also 120°.

Therefore, by using the properties of parallel lines and transversals, we can show that m∠GKB = 120°.