Answer:
An obtuse triangle has one angle larger than 90 degrees (deg). Given information, the two base angles EDF and EFD are represented by one variable x, therefore they are equal.
The sum of all angles of any triangle is 180 deg so angles EDF + EFD + DEF = 180 deg
Since the obtuse angle must be larger than 90 deg, the sum of the other two angles must be less than 90.
Angles EDF + EFD < 90 and 90 < DEF can be re written
An inequality of angles EDF + EFD < DEF
Since angles EDF and EFD are equal to x their sum is (x + x) or 2x, so we can write
2x < 90 divide both sides by 2
{0 < x < 45} is all possible values of x.
A function can be written to represent this. The function will accept input of the obtuse angle and output the two equal acute angles.
F(x) = (180 - x) / 2
where x is the measure of the obtuse angle. Only works for symmetric triangle. F(x) is the measure of each of the other two angles.
