Final answer:
To prove that ∠IKL and ∠JLD are supplementary, we rely on the given information from the Congruent Supplements Theorem and the definition of supplementary angles, which are two angles that add up to 180 degrees.
Step-by-step explanation:
To prove that ∠IKL and ∠JLD are supplementary angles, firstly, we need to use the definition of supplementary angles. Supplementary angles are two angles whose measures add up to 180 degrees. We are given that ∠IKL and ∠JLD are supplementary by the Congruent Supplements Theorem, meaning they add up to 180 degrees. If we denote m∠IKL as the measure of angle IKL and m∠JLD as the measure of angle JLD, we can write an equation as follows: m∠IKL + m∠JLD = 180° This equation aligns with the fact that the sum of measures of supplementary angles is 180°. To complete the statements to prove the angles are supplementary, we could specify if there is more known information such as if angles IKL and JLK are adjacent, forming a linear pair with ∠JLD, which would also confirm that they are supplementary. Without specific details on the positioning and relationships of these angles, the supplementary nature relies solely on the provided theorem and the equation we have established.