Q. 34.2( 22 Votes )

Three angles of a quadrilateral are in the ratio 2:3:5 and the fourth angle is 90 °. Find the measures of the other three angles.

Answer :

Let us assume a quadrilateral ABCD.



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


i.e, A + B + C + D = 3600. ...... (1)


It is also given that the first three angles are in the ratio of 2:3:5, and the fourth angle is 900.


Let us take the first three angles to be 2x, 3x and 5x.


Substituting the values in the eq(1) we get,


2x + 3x + 5x + 900 = 3600


10x = 3600 - 900


10x = 2700


x =


x = 270.


Now we find the values of the angles using the value of x.


A = 2x


A = 2 × 270


A = 540.


B = 3x


B = 3 × 270


B = 810.


C = 5x


C = 5 × 270


C = 1350.


The three angles are 540, 810, 1350.


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