Answer:
[tex]m(\widehat {RS})+m(\widehat{ST})+m(\widehat{TQ}) + m(major\ arc RQ) = 360\ degree[/tex]
Step-by-step explanation:
As we can see in the figure that
The R, S, T ,and Q are the points on the circle O.
Also
The measurement of the circular arc is equivalent to the measurement of the angle at the center of the arc
So by this
[tex]m(\widehat{RS})=m(\angle ROS)[/tex]
[tex]m(\widehat{ST})=m(\angle SOT)[/tex]
[tex]m(\widehat{TQ})=m(\angle TOQ)[/tex]
m(major arc RQ) = m(∠QOR)
So,
[tex]m(\widehat {RS})+m(\widehat{ST})+m(\widehat{TQ}) + m(major\ arc RQ) = m(\angle ROS)+m(\angle SOT)+m(\angle TOQ)+m(\angle QOR)[/tex]
And as we know that
All angles sum = 360°
Therefore
[tex]m(\widehat {RS})+m(\widehat{ST})+m(\widehat{TQ}) + m(major\ arc RQ) = 360\ degree[/tex]
