Question

If an obtuse angle is bisected, why would the two resulting angles be acute angles?

Answer 1

If `90^o < /_alpha < 180^o` then `45^o < /_alpha/2 < 90^o`.
Hence, by definition, `/_alpha/2` is acute.

Explanation:

Definitions:
Acute angle measures from `0^o` to `90^o` (endpoints of this interval are not included).
Obtuse angle measures from `90^o` to `180^o` (endpoints of this interval are not included).

Half of obtuse angle measures from `45^o` to `90^o` (not including endpoints.
All angles measured from `45^o` to `90^o` are, by definition, acute.