tests of angle bisecting skills

the three angle bisectors should meet at a point (the 'incentre')

the three centre angles are in an arithmetical progression for a 30, 60, 90 triangle

is this true whenever the triangle's angles are in arithmetical progression?

for an obtuse angled triangle
where the two interior bisectors meet the other sides
and where the exterior bisector meets the other side (produced)
should be in a straight line

(thanks to GoGeometry for this)