What's the role of androgen on menopause?

It's related. Most of the time, reduction in androgen levels (the most widely known being testosterone) occurs in similar fashion to loss of estrogen in women. Testosterone in women is made in the ovaries, the adrenal glands and from peripheral conversion (i.e. Dhea to testosterone). To name a few, testosterone regulates sex drive, muscle mass, body hair, energy levels and Insulin resistance.
Low energy, libido. Women are basically estrogen based systems, but have some testosterone. Although these testosterone levels are minimal compared to males, this hormone is important in any hrt supplementation in aging females. Labs normal range up to about 90 ng/dl. A formally available pharmaceutical preparation called estratest, (esterified estrogens and methylestosterone) used to be used. Today, your need to see a physican who prescribes bhrt including t.