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.

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.