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□PQRS IS CYCLIC m angle SPQ =7x° and m angle SRQ= 11x° m angleMPS​

Answer»

ong>□PQRS IS CYCLIC m angle SPQ =7x° and m angle SRQ= 11x° m angleSPQ

[CORRECT question]​

Given:

PQRS is a cyclic QUADRILATERAL

To find:

The measurement of the angle SPQ

Solution:

If any of the quadrilaterals is a cyclic quadrilateral,

then, by the PROPERTY of the cyclic quadrilateral, the sum of the opposite angle of the quadrilateral must be 180°.

Here we have given the angles as:

angle SPQ =7x° and angle SRQ= 11x°

and it is very CLEAR that the given angles are opposite angles so the sum of these angles must be supplementary.

so we get,

∠SPQ + ∠SRQ = 180°

7x° + 11x° = 180°

18x = 180°

x = 10°

so,

The measurement of the angle SPQ is 7x = 7×10 = 70°


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