Question

7. In quadrilateral PORS angle P = 5x, Angle Q= 3x, angle R= 4x and angle
S = 6x. Then the measure of the greatest angle of
quadrilateral PQRS.​

Answer 1

$Given \: in \: Quadrilateral \: PQRS ,\\\angle P = 5x , \: \angle Q = 3x , \: \angle R = 4x ,\\and \: \angle R = 4x$

$\underline {\blue { By \: Angle \:Sum \: Property : }}$

$\pink { Sum \:of \: 4 \:angles \: in \: Quadrilateral }$

$\pink {are \: supplementary }$

$\implies \angle P + \angle Q + \angle R + \angle S = 360\degree$

$\implies 5x + 3x + 4x + 6x = 360\degree$

$\implies 18x = 360\degree$

$\implies x = \frac{360}{18}$

$\implies x = 20$

/* Putting x = 20 */

$\angle P = 5x = 5\times 20 = 100\degree$

$\angle Q = 3x = 3\times 20 = 60\degree$

$\angle R = 4x = 4\times 20 = 80\degree$

$\angle S = 6x = 6\times 20 = 120\degree$

$Greatest \: angle \: of \: Quadrilateral \:PQRS \\ is \: \angle S$

Therefore.,

$\red {Greatest \: angle \: of \:PQRS}\green { = \angle S }$

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