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 **360 ^{0}**.

i.e, **∠****A +** **∠****B +** **∠****C +** **∠****D = 360 ^{0}**. ...... (1)

It is also given that the first three angles are in the ratio of **2:3:5**, and the fourth angle is **90 ^{0}**.

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 + 90^{0} = 360^{0}

⇒ 10x = 360^{0} - 90^{0}

⇒ 10x = 270^{0}

⇒ x =

⇒ **x = 27 ^{0}**.

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

⇒ ∠A = 2x

⇒ ∠A = 2 × 27^{0}

⇒ **∠****A = 54 ^{0}**.

⇒ ∠B = 3x

⇒ ∠B = 3 × 27^{0}

⇒ **∠****B = 81 ^{0}**.

⇒ ∠C = 5x

⇒ ∠C = 5 × 27^{0}

⇒ **∠****C = 135 ^{0}**.

The three angles are **54 ^{0}, 81^{0}, 135^{0}**.

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