The angles P, Q, R and S of a trapezium PQRS are in the ratio 1:3:7:9. Match the angle to its correct value.

162 °

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126 °

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18 °

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54 °

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Solution

As the angles are in the ratio 1:3:7:9
We can take the angles as $x$ , $3 x$ , $7 x$ and $9 x$ .
$x + 3 x + 7 x + 9 x = 360^{\circ}$
$\Rightarrow 20 x = 360^{\circ}$
$\Rightarrow x = 18^{\circ}$
$∠ P = x = 18^{\circ}$ ,
$∠ Q = 3 x = 54^{\circ}$
$∠ R = 7 x = 126^{\circ}$
$∠ S = 9 x = 162^{\circ}$

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The angles P, Q, R and S of a trapezium PQRS are in the ratio 1:3:7:9. Match the angle to its correct value.

As the angles are in the ratio 1:3:7:9 We can take the angles as x, 3x, 7x and 9x. x+3x+7x+9x=360∘ ⇒20x=360∘ ⇒x=18∘ ∠P=x=18∘, ∠Q=3x=54∘ ∠R=7x=126∘ ∠S=9x=162∘