Question

prove that the angle in a segment shorter than a semicircle is greater than a right angle.

Answer 1

QP is a major arc and is greater than PSQ is the angle formed by it in the alternate segment.  

We know that, the angle subtended by an arc at the center is twice the angle subtended by it at any point of the alternate segment of the circle. 

2 <PSQ = m 

QP  

2<PSQ = 360 Degrees – m  

PQ 

2<PSQ= 360 - <POQ 

2<PSQ= 360 – 180 Degrees 

2<PSQ>180 

<PSQ> 90 

The angle in a segment shorter than a semi-circle is greater than a right angle