Question

In quadrilateral pqrs angleR = 60° find the ratio R:Q

Answer 1

Given, that PQRS is a qudrilateral

Adjacent angles of a quadrilateral are supplementary, i.e., they add upto 180°

Given, ∠R = 60°

∠Q is adjacent to ∠R. So they both are supplementary angles


So,

∠Q + ∠R = 180

∠Q = 180 - ∠R

∠Q = 180 - 60

∠Q = 120°

m∠Q is 120°


To find the ratio of ∠R : ∠Q

m∠R : m∠Q

60 : 120

By reducing we get

1 : 2



∴ ∠R : ∠Q = 1 : 2

Answer 2

Thank you for asking this question. Here is your answer

We will assume the ratio of angle R to Q  1 : 2

We know this from the question that PQRS is a quadrilateral:

So keeping that in mind we will solve the question:

<R=60

Now we will find <Q

<Q and <R are supplementary (reason: <Q is an adjacent angle of <R)

So, <Q + <R is equal to 180

<Q = 180 - <R

= 180 - 60

= 120

Now we will find the ratio of angle R in terms of Q

<R : <Q = 60 : 120

= 1: 2

So the final answer for this question is 1:2

If there is any confusion please leave a comment below.