Question 62

PQRS is a cyclic quadrilateral. If angle P is three times the angle R and angle S is five times the angle Q,then the sum of the angles Q and R is:

Solution

By the formation of cyclic quadrilateral we know the sum of opposite angles is 180.

P+R=180-----<1>

So putting the value of P and R we get,

3x+x=180, I.e x=45 degree

and Q+S=180---<2>

then, 5y+y=180, i.e y=30 degree

So P=135 degree, Q=30 degree, R=45 degree, S=150 degree.

Q+R=45+30=$$75^\circ$$

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