Question

△jln and △klm are shown below.
which statement is true?
△jln is similar to △klm.
△jln is not similar to △klm.
there is not enough information to determine whether the triangles are similar.

Explanation:

Step1: Calculate ∠KML

∠KML = 180° - 38° = 142°

Step2: Calculate ∠JKL in △KLM

∠JKL = 180° - 120° - 38° = 22°

Step3: Calculate ∠JNL in △JLN

∠JNL = 180° - 22° - ∠JLN
Since ∠JLN = 120° (shared angle), ∠JNL = 180° - 22° - 120° = 38°

Step4: Compare triangle angles

△JLN has angles 22°, 120°, 38°; △KLM has angles 22°, 120°, 38°. All corresponding angles are equal.

Answer:

△JLN is similar to △KLM.