The electron-domain geometry and molecular geometry of iodine trichloride are __________ and __________, respectively.

The answer is trigonal bipyramidal, T-shaped, respectively- I do not understand the approach

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i don't understand how you got that though? That is the answer though.
Here is a site that shows the Lewis structure for ICl3. Using that, look in your text for the geometry of AB3U2 to find the shape.