The following figure is a rectangle in which x : y = 3 : 7; find the values of x and y.

It is given that ABCD is a rectangle in which x : y = 3 : 7.

Let ∠ BEC be 3a and ∠ BCE = 7a

In triangle BEC, sum of all the angles is 180°.

⇒ ∠ BEC + ∠ BCE + ∠ CBE = 180°

⇒ 3a + 7a + 90° = 180° (each angle of rectangle is 90°)

⇒ 10a + 90° = 180°

⇒ 10a = 180° - 90°

⇒ 10a = 90°

⇒ a = $\dfrac{90°}{10}$

⇒ a = 9°

So, ∠ BEC = x = 3 $\times$ 9° and ∠ BCE = y = 7 $\times$ 9°

⇒ x = 27° and y = 63°

Hence, the value of x = 27° and y = 63°.