Question

Draw an obtuse angle. Bisect it. Measure each of the angles so obtained.

Answer 1

Obtuse angles are those angles which are greater than 90° but less than 180°.
Draw an obtuse angle ∠BAC.
With an appropriate radius and centre at A, draw an arc such that it intersects AB and AC at P and Q, respectively

With centre P and radius more than half of PQ, draw an arc.
With the same radius and centre at Q, draw another arc intersecting the previous arc at R.
Join A and R and extend it to X.
The ray AX is the required bisector of ∠BAC.
If we measure ∠BAR and ∠CAR, we have
∠BAR = ∠CAR = 65°

Note: Bisected Angle so obtained may be different When your obtuse angle is different from this obtuse angle.