**Hint:** PQRS is a quadrilateral. The property of quadrilateral says that the sum of any two angles is 180 . All the internal angles of a quadrilateral sum up to ${360^ \circ }$. In this question first we have to find the value of angle Q then we simply can't get the ratio of angle R and angle Q.

**Complete step-by-step answer:**

We known that \[\angle R + \angle Q = {180^ \circ }\]

And we have the value of angle R is given $\angle R = {60^ \circ }$

Simply put the value of angle R

= ${60^ \circ } + \angle Q = {180^ \circ }$

= $\angle Q = {180^ \circ } - {60^ \circ }$

= $\angle Q = {120^ \circ }$

Now we have the value of angle Q

We can easily find the ratio of angle R and angle Q

For finding the ratio just do $\dfrac{{\angle R}}{{\angle Q}}$

= $\dfrac{{\angle R}}{{\angle Q}}$$ = \dfrac{{60}}{{120}}$

By canceling the denominator and numerator we get

= $\dfrac{{\angle R}}{{\angle Q}}$$ = \dfrac{1}{2}$

Here we get ratio of angle R and angle Q is 1:2

**Note:** Quadrilateral just means “four side”. A quadrilateral has four sides, it has two dimensional, closed and has straight sides. All the internal angles of a quadrilateral sum up to ${360^ \circ }$. And the most important point is opposite angles are equal and opposite sides are equal and parallel. In quadrilateral sum of any two adjuacent angles is $180$. In quadrilateral if one angle is the right angle then all the angles are the right angle and the diagonals of a parallelogram bisect each other. According to the angle sum property of a quadrilateral, the sum of all the four interior angles is equal to ${360^ \circ }$.