Question

please help me to solvethis​

Answer 1

Answer:

The answer is 34 according to the bisector property of triangles on the same base see ex.5.4 ncert maths book last question class 9

Step-by-step explanation:Given: ABC is a triangle,

In which  

Also, BE and CE are the angle bisector of the angles ABC and ACD,

We have to prove that: ∠BEC = 1/2 ∠BAC

Proof:

BE is the angle bisector of angle ABC,

⇒ ∠ABE = ∠EBC

And, CE is the angle bisector of angle ACD,

⇒ ∠ACE = ∠ECD

By the exterior angle theorem,

∠ACD = ∠ABC + ∠BAC

⇒ (∠ACE + ∠ECD) = (∠ABE + ∠EBC) + ∠BAC

⇒ 2∠ECD = 2∠EBC + ∠BAC

⇒ ∠BAC = 2(∠ECD - ∠EBC) ---------(1)

Now, again by exterior angle theorem,

∠ECD = ∠EBC+∠BEC

⇒ ∠BEC = ∠ECD - ∠EBC ------------(2)

By equation (1) and (2),

∠BAC = 2 ∠BEC

⇒ 1/2 ∠BAC = ∠BEC

Hence, proved.

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Answer 2

Answer:

34°

Step-by-step explanation:

let, angle ABC = 2x and angle ACD = 2y

since, BE was bisector, angle ABE = angle EBC = 2x/2 = x

since, CE was bisector, angle ACE = angle ECD = 2y/2 = y

angle ABC + angle BAC = angle ACD (exterior angle property)

⇒ 2x + 68 = 2y  ⇒ x - y = -34

angle BCE + angle ECD = 180 (linear pair)

⇒ angle BCE = 180 - y

in triangle BCE

angle EBC + angle BCE + angle BEC = 180 (angle sum property)

⇒ x + 180 - y + angle BEC = 180

⇒ x - y = - (angle BEC)

⇒ - 34 = - (angle BEC)

⇒ angle BEC = 34°