Question

Please answer this with a step-by-step solution and reasons

Answer 1

Answer:

∠DEB=24°

⇒∠BEC = 36°

Step-by-step explanation:

We have ABCD as the given rhombus.

Now, ∠BCD = ∠BAD = 46°   (Opposite angles of rhombus are equal)

Now, CED is an equilateral Δ.

Now, ∠DEC = ∠ECD = ∠CDE = 60°

In ΔBCE,      

CE = CB  [Given]⇒∠CBE = ∠CEB  (Angles opposite to equal sides are equal)

In ΔBEC,

∠CBE + ∠CEB + ∠ECB = 180°   (angle sum property)⇒

2∠BEC + 60° + 46° = 180°

⇒2∠BEC = 72°

⇒∠BEC = 36°

∠BEC+∠DEB = ∠DEC

36°+∠DEB = 60°

∠DEB=60°-36°

∠DEB=24°