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Yes.

If an angle of x degree is obtuse then x > 180 deg

Suppose x = 180 + y where y is positive.

Then x can be divided into two angles of 90+y/2 degrees each

y>0 so 90 + y/2 > 90

and so the two angles are obtuse.

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Q: Can all reflex angles can be divided into 2 obtuse angles?
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