Questions: The diagram below shows isosceles trapezoid KEMN. To find the value of x, Alicia wrote the following steps. What reason justifies step 3? 1. m angle LKN + m angle KNM = 180 degrees 2. m angle LKN = 48 degrees 3. 48 = 2x + 10 4. 38 = 2x 5. 19 = x A. The base angles in an isosceles trapezoid are supplementary. B. The adjacent angles between the parallel sides are supplementary. C. The base angles of an isosceles trapezoid are congruent. D. The opposite angles in an isosceles trapezoid are congruent.

Solution Steps

Alicia's steps are aimed at finding the value of x in the expression (2x + 10) which represents the measure of angle LMN. Step 1 establishes that angles LKN and KNM are supplementary (add up to 180 degrees). Step 2 determines the measure of angle LKN. Step 3 sets up an equation using the value found in Step 2.

Step 3 states 48 = 2x + 10. This step sets the measure of angle LKN (found to be 48°) equal to the expression representing the measure of angle LML, which is (2x + 10).

The justification for Step 3 is that it uses the property that the base angles of an isosceles trapezoid are congruent. In the given isosceles trapezoid KLMN, angles LKN and LML are base angles and hence have equal measure. This allows us to set their expressions equal to each other in step 3.

Final Answer: C. The base angles of an isosceles trapezoid are congruent.