Question

In the given figure, if OP stands on the line QR
such that angle POR: angle QOP = 4:5, show that angle QOP - angle POR = 1/2 angle QOR.
​

Answer 1

See the photo attached for solution

Answer 2

$\angle { POR} : \angle {QOP} = 4 : 5$

$Let \: \angle { POR} = 4x$

$and \: \angle { QOP} = 5x$

/* We know that */

$\angle { POR} + \angle { QOP} = 180\degree$

$\blue{ ( Linear \: pair ) }$

$\implies 4x + 5x = 180$

$\implies 9x = 180$

$\implies x = \frac{180}{9}$

$\implies x = 20 \: --(1)$

$LHS= \red{ \angle { QOP} - \angle { POR} }$

$= 5x - 4x$

$= x$

$= 20$

$RHS = \frac{\angle { QOR}}{2}$

$= \frac{ \angle { POR} + \angle { QOP}}{2}$

$= \frac{180}{2}$

$= 90\degree$

Therefore.,

$LHS \neq RHS$

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