Q1 of 28 Page 122

Two angles of a quadrilateral are 70° and 130° and the other two angles are equal. Find the measure of these two angles.


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


Let us consider Quadrilateral ABCD,


Let ∠A = 700 and ∠B = 1300 ,


According to the problem, it is told that the remaining two angles are equal,


i.e, ∠C = ∠D


∴∠A + ∠B + ∠C + ∠D = 3600


Now substituting the values and conditions we get,


⇒ 700 + 1300 + ∠C + ∠C = 3600


⇒ 2000 + 2 × ∠C = 3600


⇒ 2 × ∠C = 3600 - 2000


⇒ 2 × ∠C = 1600



⇒ ∠C = 800


The values of the other two angles is700, 700.


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