In given figure $□$ PQRS is an Isosceles trapezium.Side PQ $∥$ side SR and $△$ RQE is an equilateral triangle; find the measures of all the angles of the trapezium.

60^{\circ}, 50^{\circ}, 120^{\circ}, 170^{\circ}

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60^{\circ}, 40^{\circ}, 120^{\circ}, 150^{\circ}

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60^{\circ}, 80^{\circ}, 120^{\circ}, 190^{\circ}

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60^{\circ}, 60^{\circ}, 120^{\circ}, 120^{\circ}

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Solution

The correct option is D $60^{\circ}, 60^{\circ}, 120^{\circ}, 120^{\circ}$
$I n e q u i l a t e r a l △ E R Q, ∠ R E Q = ∠ E Q R = ∠ Q R E = 60^{o} G i v e n P Q ∥ S R, l e t R Q b e t h e t r a n s v e r s a l t h e n ∠ S R Q + ∠ R Q P = 180^{o} {S u m o f I n t e r i o r c o r r e s p o n d i n g a n g l e s = 180^{o}} S o w e g e t ∠ S R Q = 180 - 60 = 120^{o} {∠ R Q P = ∠ E Q R = 60^{o}} W e k n o w t h a t i n a i s o s c e l e s t r a p e z i u m b a s e a n g l e s a r e e q u a l . S o ∠ S P Q = ∠ R Q P = 60^{o} G i v e n P Q ∥ S R, l e t S P b e t h e t r a n s v e r s a l t h e n ∠ R S P + ∠ S P Q = 180^{o} {S u m o f I n t e r i o r c o r r e s p o n d i n g a n g l e s = 180^{o}} S o w e g e t ∠ R S P = 180 - 60 = 120^{o} ∴ T h e m e a s u r e s o f t h e t r a p e z i u m a r e : ∠ R S P = 120^{o}, ∠ S R Q = 120^{o}, ∠ R Q P = 60^{o}, ∠ Q P S = 60^{o}$

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Class Intervals	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$
Frequency	$120$	?	$200$	?	$185$
Cumulative Frequency	$120$	?	?	?	$900$

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Q. Question 30
In a parallellogram PQRS, if

∠ P = 60^{\circ}

, then other three angles are
a)

45^{\circ}, 135^{\circ}, 120^{\circ}

60^{\circ}, 120^{\circ}, 120^{\circ}

60^{\circ}, 135^{\circ}, 135^{\circ}

45^{\circ}, 135^{\circ}, 135^{\circ}

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In given figure □ PQRS is an Isosceles trapezium.Side PQ ∥ side SR and △RQE is an equilateral triangle; find the measures of all the angles of the trapezium.

In given figure $□$ PQRS is an Isosceles trapezium.Side PQ $∥$ side SR and $△$ RQE is an equilateral triangle; find the measures of all the angles of the trapezium.