Question

3)In a quadrilateral PQRS. PQ||RS. ∠P : ∠S= 5:7 and ∠Q: ∠R = 7:5. Find the measure of each interior angle of

the quadrilateral.​
plss send working
with diagram

Answer 1

Hello mate..

$\huge❁ \underbrace\mathfrak \pink{solution}❁$

GIVEN:

∠P : ∠S = 5:7

∠Q : ∠R = 7:5

∠P = 5x

∠S = 7x

∠Q = 7x

∠R = 5x

We know that,

$\bold \green{sum \: of \: all \: interior \: angles \: in \: a \: quadrilateral = 360°}$

Then,

$\bold{5x + 7x + 7x + 5x = 360} \\ \bold{10x + 14x = 360} \\ \bold{24x = 360} \\ \bold{x = \frac{360}{24} } \\ \bold{x = 15}$

Therefore,

∠P = 5x = 5 × 15

=> 75°

∠S = 7x = 7 × 15

=> 105°

∠Q = 7x

=> 105°

∠R = 5x

=> 75°

Therefore, the interior angles are 75°, 105°, 75°, 105°.

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HOPE THIS HELPS YOU..