In the given figure, O is the centre of a circle, chord PQ ≅ chord RS

Explanation:- 

The problem gives us a circle with center O. Chords PQ and RS are given as congruent. We need to find the measure of arc QSR.

First, we know that congruent chords of a circle have congruent arcs. Therefore, arc PQ is congruent to arc RS. Thus, the measure of arc PQ is 80 degrees.

Next, we know that the measure of a minor arc is equal to its central angle. Since arc PR is a minor arc, we can say that the measure of arc PR is equal to the measure of angle POR, which is 70 degrees.

Now, using the fact that the sum of the measures of the four arcs formed by the chords of a circle is equal to 360 degrees, we can set up an equation:

measure of arc PR + measure of arc PQ + measure of arc QS + measure of arc RS = 360 degrees

Substituting the values we have found so far, we get:

70 degrees + 80 degrees + measure of arc QS + 80 degrees = 360 degrees

Simplifying, we get:

measure of arc QS = 360 degrees – 230 degrees = 130 degrees

Finally, we can find the measure of arc QSR by using the fact that the measure of an arc formed by two chords is equal to the sum of the measures of the two arcs that the chords divide the circle into. Therefore, we have:

measure of arc QSR = measure of arc QS + measure of arc RS = 130 degrees + 80 degrees = 210 degrees.

Hence, we have found that the measure of arc QSR is 210 degrees.