Question

not to scale
which triangles are similar to △efg?
none
only △hij
only △klm
△hij and △klm

Explanation:

Step1: Find angle in △EFG

In triangle \( EFG \), we know two angles: \( \angle E = 42^\circ \) and \( \angle F = 87^\circ \). The sum of angles in a triangle is \( 180^\circ \), so \( \angle G=180^\circ - 42^\circ - 87^\circ = 51^\circ \). So angles of \( \triangle EFG \) are \( 42^\circ \), \( 87^\circ \), \( 51^\circ \).

Step2: Analyze △HIJ

In \( \triangle HIJ \), angles are \( \angle J = 51^\circ \), \( \angle H = 42^\circ \). Then \( \angle I=180^\circ - 51^\circ - 42^\circ = 87^\circ \). Angles: \( 51^\circ \), \( 42^\circ \), \( 87^\circ \), same as \( \triangle EFG \).

Step3: Analyze △KLM

In \( \triangle KLM \), angles are \( \angle L = 87^\circ \), \( \angle N = 51^\circ \) (wait, label is \( KLM \), so \( \angle L = 87^\circ \), \( \angle M = 51^\circ \), then \( \angle K=180^\circ - 87^\circ - 51^\circ = 42^\circ \). Angles: \( 87^\circ \), \( 51^\circ \), \( 42^\circ \), same as \( \triangle EFG \).

Answer:

\( \triangle HIJ \) and \( \triangle KLM \) (corresponding option: \( \triangle HIJ \) and \( \triangle KLM \))