Question

In PQRS, ∠ R = 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