Question

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

Explanation:

Step1: Find ∠KOL's right angle

$\angle K = 90^\circ$ (given right angle in $\triangle KOL$)

Step2: Calculate ∠KLO in △KOL

Sum of angles in triangle is $180^\circ$.
$\angle KLO = 180^\circ - 90^\circ - 47^\circ = 43^\circ$

Step3: Match angles in both triangles

In $\triangle KMN$: $\angle K = 90^\circ$, $\angle N = 43^\circ$, so $\angle M = 180^\circ - 90^\circ - 43^\circ = 47^\circ$.
In $\triangle KOL$: $\angle K = 90^\circ$, $\angle KOL = 47^\circ$, $\angle KLO = 43^\circ$.
All corresponding angles are equal.

Answer:

$\triangle KMN$ is similar to $\triangle KOL$.