Question

in the adjoining figure ABCD is a rectangle if angle CEB : angle ECB = 3:2, find angle DCF

Answer 1

Answer is 126°
Here's the solution

Answer 2

Answer:

∠DCF = 126°

Step-by-step explanation:

Since, ABCD is a rectangle so each angle is of 90°

⇒ ∠ABC = 90°

∠CEB : ∠ECB = 3:2

Let ∠CEB = 3x and ∠ECB = 2x

Now, in ΔCEB using angle sum property of the triangle

⇒ ∠EBC + ∠CEB + ∠ECB = 180°

⇒ 90 + 3x + 2x = 180

⇒ 5x = 90

⇒ x = 18

So, ∠CEB = 54° and ∠ECB = 36°

Now, ∠BCD = 90° ( Angle of rectangle)

⇒ ∠ECB + ∠ECD = 90°

⇒ 36 + ∠ECD = 90

⇒ ∠ECD = 54°

Now, ∠ECD + ∠DCF = 180 ( Linear pair)

⇒ 54 + ∠DCF = 180

⇒ ∠DCF = 126°