Question

in figure 5 ABCD is a rectangle if angle CEB:angle ACB=3:2 find the measure of angle AEC and angle CEB

Answer 1

Let ∠CEB = 3x; ∠ECB = 2x 
In ΔCBE, 
∠CEB + ∠ECB + ∠EBC = 180°  [angle sum property]
⇒3x+2x+90° = 180°
⇒5x = 90°
⇒x = 18 
So,  ∠CEB = 3×18 = 54°; ∠ECB = 2×18 = 36°
Now, ∠ECD = 90° − ∠ECB = 90° − 36° = 54°
Now, ∠DCF + ∠ECD = 180°  [Linear pair]
⇒∠DCF + 54° = 180°
⇒∠DCF = 180°−54° = 126°

Answer 2

Answer:

Step-by-step explanation:

Let ∠CEB = 3x; ∠ECB = 2x

In ΔCBE,

∠CEB + ∠ECB + ∠EBC = 180°  [angle sum property]

⇒3x+2x+90° = 180°

⇒5x = 90°

⇒x = 18

So,  ∠CEB = 3×18 = 54°; ∠ECB = 2×18 = 36°

Now, ∠ECD = 90° − ∠ECB = 90° − 36° = 54°

Now, ∠DCF + ∠ECD = 180°  [Linear pair]

⇒∠DCF + 54° = 180°

⇒∠DCF = 180°−54° = 126°