Question

In the given figure, chord PQ and chord RS intersect at point T. Then complete the following activity to prove, 

∠STQ = `1/2` [m(arc SQ) + m(arc PR)]

Activity:

∠STQ = ∠SPQ + `square`    ...(Remote interior angles theorem of a triangle)
`1/2` m(arc PQ) + `square`    ...(Inscribed angle theorem)

=`1/2 [square + square]`

Answer 1

∠STQ = ∠SPQ + \[\boxed{\angle{\text{PSR}}}\]      ...(Remote interior angles theorem of a triangle)

= \[\frac{1}{2}m(\text{arc SQ}) + \boxed{\frac{1}{2}m(\text{arc PR})}\]       ...(Inscribed angle theorem)

= \[\frac{1}{2}\]\[\begin{bmatrix}\boxed{m(\text{arc  SQ})}+\boxed{m(\text{arc  PR})}\end{bmatrix}\]