The figure may be labelled as shown.
The simplest triangles are AKI, AIL, EKD, LFB, DJC, BJC, DHC and BCG i.e. 8 in number.
The triangles composed of two components each are AKL, ADJ, AJB and DBC i.e. 4 in number.
The triangles composed of the three components each are ADC and ABC i.e. 2 in number.
There is only one triangle i.e. ADB composed of four components.
Thus, there are 8+ 4 + 2 + 1= 15 triangles in the figure.