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The largest angle of the quadrilateral PQRS is 120°
<u>Step-by-step explanation:</u>
Given that
3P=2Q (1)
4Q=3R
Q=3R/4
Substitute the value of <Q in (1)
<P=3R/6=R/2
Comparing (1) and (2)
we get 6P=4Q=3R
In a cyclic quadrilateral, opposite angles are supplementary i.e their sum is 180 degree
<P and <R are opposite angles.
Hence
<R/2+<R=180
<S and <Q are opposite angles. Hence
<S=180-<Q=180-90=90°
<P=60°
<Q=90°
<R=120°
<S=90°
The largest angle of the quadrilateral is 120°(<R)