Question

the diagram below shows isosceles trapezoid klmn.
to find the value of x, alicia wrote the following steps. what reason justifies step 3?

1. ( mangle lkn + mangle knm = 180^circ )
2. ( mangle lkn = 48^circ )
3. ( 48 = 2x + 10 )
4. ( 38 = 2x )
5. ( 19 = x )

options:

• the opposite angles in an isosceles trapezoid are congruent.
• the base angles in an isosceles trapezoid are supplementary.
• the adjacent angles between the parallel sides are supplementary.
• the base angles of an isosceles trapezoid are congruent.

Explanation:

In an isosceles trapezoid, the base angles (angles adjacent to each base) are congruent. Step 3 sets \(48 = 2x + 10\), which implies \(\angle LKN = \angle KLM\) (both base angles for the top base \(KL\)). This equality is justified by the congruence of base angles in an isosceles trapezoid.

Answer:

The base angles of an isosceles trapezoid are congruent.