Question

are these triangles similar?
j
k
i
57°
86°
f
e
g
50°
86°

Explanation:

Step1: Calculate the third angle of triangle \( \triangle JKI \)

The sum of angles in a triangle is \( 180^{\circ} \). Let the third angle be \( \angle I \).
\( \angle I=180^{\circ}-(86^{\circ} + 57^{\circ})=180^{\circ}-143^{\circ}=37^{\circ} \)

Step2: Calculate the third angle of triangle \( \triangle FGE \)

Let the third angle be \( \angle G \).
\( \angle G=180^{\circ}-(50^{\circ}+86^{\circ})=180^{\circ}-136^{\circ} = 44^{\circ} \)

Step3: Check for similarity

For two triangles to be similar, their corresponding angles must be equal.
In \( \triangle JKI \), angles are \( 86^{\circ},57^{\circ},37^{\circ} \)
In \( \triangle FGE \), angles are \( 50^{\circ},86^{\circ},44^{\circ} \)
Since the angles are not equal, the triangles are not similar.

Answer:

no