Q2 of 28 Page 122

In the fig, suppose ∠P and ∠Q are supplementary angles and ∠R = 125° . Find the measures of ∠S.

According to the problem it is given that,


∠R = 1250 and ∠P and ∠Q are supplementary angles.


We know that, the sum of supplementary angles equals to 1800.


So, ∠P + ∠Q = 1800.


We know that the sum of all angles in a quadrilateral is 3600.


So, ∠P + ∠Q + ∠R + ∠S = 3600.


Substituting the values and conditions we obtain,


⇒ 1800 + 1250 + ∠S = 3600


⇒ 3050 + ∠S = 3600


⇒ ∠S = 3600 - 3050


⇒ ∠S = 550.


The value of ∠S is550.


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