Question

In the figure, if the chord PQ and chord RS intersect at point T.

Prove that m∠STQ = `1/2` [m(arc PR) + m(arc SQ)] for any measure of ∠STQ by filling out the boxes.

Proof: m∠STQ = m∠SPQ + `square`   ...[Theorem of the external angle of a triangle]

 = `1/2` m(arc SQ) + `square`   ...[Inscribed angle theorem]

= `1/2 [square + square]`

Answer 1

m∠STQ = m∠SPQ + \[\boxed{\text{m∠PSR}}\]   ...[Theorem of the external angle of a triangle]

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

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