Question

Complete the following proof. Given: Points R, S, T, Q on circle O Prove: m\overarc RS + m\overarc ST + m\overarc TQ + m\overarc RQ

Answer 1

Answer:

360°

Step-by-step explanation:

From the figure attached,

R, S, T and Q are the points on a circle O.

Since, "measure of an arc of a circle is equal to the measure of the angle subtended by the arc at the center."

By this statement,

$m(\widehat{RS})=m(\angle ROS)$

$m(\widehat{ST})=m(\angle SOT)$

$m(\widehat{TQ})=m(\angle TOQ)$

m(major arc RQ) = m(∠QOR)

Now $m(\widehat {RS})+m(\widehat{ST})+m(\widehat{TQ})$ + m(major arc RQ) = $m(\angle ROS)+m(\angle SOT)+m(\angle TOQ)+m(\angle QOR)$

Since sum of all angles at a point = 360°

$m(\widehat {RS})+m(\widehat{ST})+m(\widehat{TQ})$ + m(major arc RQ) = 360°