Question

In cyclic quadrilateral PQRS,

Answer 1

The largest angle of the quadrilateral PQRS is 120°

Step-by-step explanation:

Given that

$\frac{\angle P}{2} =\frac{\angle Q}{3}=\frac{\angle R}{4}$

3P=2Q   (1)

4Q=3R

Q=3R/4

Substitute the value of <Q in (1)

$3P=2(\frac{3R}{4} )=\frac{3R}{2} \\6P=3R\ -->(2)$

<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

$\frac{3R}{2} =180\\R=120\°$

<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)