This is the 17410th most frequent Turkish word.
üçgenindeki
"Belonging to or in the triangle."
Here, 'üçgenindeki' refers to a possessive construction indicating 'in the triangle of (something)' which is 'matematik kitabındaki' (in the mathematics book).
Matematik kitabındaki üçgenindeki açıları ölçtün mü?
Have you measured the angles in the triangle in the mathematics book?
In this sentence, 'üçgenindeki' specifies a location or component belonging to 'haritadaki' (on the map).
Haritadaki üçgenindeki mesafeyi hesapladık.
We calculated the distance in the triangle on the map.
Here, 'üçgenindeki' identifies the triangle contained within 'sanat eserindeki' (in the artwork).