Make me an upside-down Christmas tree!
Python 3, 127 121 105 103 100 98 bytes

This is an unnamed lambda function which returns a list of lines:



lambda o:[s.center(o)for s in['___','\ /','|',*[f'&lt;{"-"*(o-i+2-i%2*3)}&gt;'for i in range(4,o)],'*']]


Try it online!

The main part of this answer is (o-i+2-i%2*3), which works out the number of dashes to have on a line. The rest of the answer is simply converting this into the desired ASCII-art.

Many thanks to Mr. Xcoder, for shaving 6 bytes, and discussing golfs with me in chat. 

Thanks also to Lynn for noticing that 3*(i%2) can be i%2*3, 2 bytes shorter!