Question

show that the angle in minor segment is an obtuse angle and the angle in the major segement is an acute angle

Answer 1

angle suspended at an arc of circle is double to any other angle
so
2∠PRQ is less than 180 degree
so, ∠PRQ is less than 90 degree
therefore, ∠PRQ is an acute angle

as QP is the major arc and ∠PSQ is the angle formed by the alternate segment
2∠PSQ = m (arc PQ)
2∠PSQ =360-  m (arc PQ)
2∠PSQ = 360 - ∠POQ
2∠PSQ is greater than 360 -180
∠PSQ is greater than 90 
so it is obtuse 

Answer 2

Step-by-step explanation:

PSQ is major segment. and PRQ is minor segment in the circle.

we have to prove: angle prq is acute and   psq is obtuse.

* Draw  op, oq and pq.

We know that-- angle suspended by arc of circle at center is twice the angle suspended at any point on remaining part of the circle.

so, ∠ poq =2∠prq

but  ,  2∠ poq <180° (∵ ∠ of Δpoq)

∠poq<90°.  ----> acute angle.

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now reflex angle poq = 2∠psq

but ∠ poq >180°.

so 2∠psq >180°

     ∴∠psq>90°  ---->obtuse angle.