Q1 of 28 Page 124

In a trapezium PQRS, PQ ║ RS; and ∠P = 70° and ∠Q = 80°. Calculate the measure of ∠S and ∠R.

Let us consider trapezium PQRS with PQ||RS.


According to the problem, it is given that ∠P = 700and ∠Q = 800.



We know that the sum of adjacent angles between two parallel lines is 1800.


i.e, ∠P + ∠S = 1800 ...... - - (1)


∠Q + ∠R = 1800. ...... - (2)


Substituting the value of ∠P in eq(1) we get,


⇒ 700 + ∠S = 1800


⇒ ∠S = 1800 - 700


⇒ ∠S = 1100.


Substituting the value of ∠Q in eq(2) we get,


⇒ 800 + ∠R = 1800


⇒ ∠R = 1800 - 800


⇒ ∠R = 1000.


The values of ∠S and ∠R is1100 and 1000.


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