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Condition for Two Lines to Be Parallel

If angle P, Q...

Question

If angle P, Q, R and S of the quadrilateral pqrs taken in order, are in ratio 5 ratio 7 ratio6:9 then find the respective angles.

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Solution

$G i v e n P : Q : R : S = 5 : 7 : 6 : 9$
Let $P = 5 x, Q = 7 x, R = 6 x, S = 9 x$
$P + Q + R + S = 27 x = 2 π ⟹ x = \frac{2 π}{27}$
$P = \frac{10 π}{27}, Q = \frac{14 π}{27}, R = \frac{4 π}{9}, S = \frac{2 π}{3}$

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