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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