Question

# In quadrilateral PQRS , $\angle R={60^\circ}$. Find the ratio of $\angle R$ to $\angle Q$.

Verified
131.1k+ views
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.

We known that $\angle R + \angle Q = {180^ \circ }$
And we have the value of angle R is given $\angle R = {60^ \circ }$
= ${60^ \circ } + \angle Q = {180^ \circ }$
= $\angle Q = {180^ \circ } - {60^ \circ }$
= $\angle Q = {120^ \circ }$
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}$
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 ${360^ \circ }$.