Question

if two consecutive angles of a cyclic quadrilateral ar ‘x’ and ‘180 – 2x’ . find other two angles.

Answer 1

The other two angles are $2x\text{ and }180^\circ-x$

Step-by-step explanation:

Given: if two consecutive angles of a cyclic quadrilateral are ‘x’ and ‘180 – 2x’

In the figure (attachment)

$\angle SPQ=x$

$\angle PQR=180-2x$

$\angle PSR=y$

$\angle SRQ=z$

In a cyclic quadrilateral, Angle sum property of quadrilateral.

$\angle SPQ+\angle PQR+\angle PSR+\angle S=360^\circ$

$x+180-2x+y+z=360^\circ$

$-x+y+z=180^\circ\ \ \ \ ...(i)$

$\angle PQR+\angle PSR=180^\circ$      $\because PQRS\text{ is cyclic quadrilateral}$

$180-2x+y=180^\circ$

$y=2x$

$\angle SPQ+\angle SRQ=180^\circ$      $\because PQRS\text{ is cyclic quadrilateral}$

$x+z=180^\circ$

$z=180-x$

Hence, the other two angles are $2x\text{ and }180-x$

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