Question

in the given figure is equal to a AB=Ac ,angle BAC = 40 degree angle a c f = 75 degree and BC is a line and prove that be is equal to Ce

Answer 1

Answer:

Step-by-step explanation:

Using exterior angle property, ∠ACF=∠ABC+∠BAC

⇒75°=∠ABC+40°

⇒∠ABC=35°

Also, we are given that AE=AC⇒∠AEC=∠ACE

In ΔACE, we have

∠AEC+∠EAC+∠ACE=180°(Sum of all the angles of a triangle=180°)

⇒2∠AEC=180°-40°

⇒∠AEC=70°

Also, using the straight angle property, ∠BCE+∠ACE+∠ACF=180°

⇒∠BCE+70°+75°=180°

⇒∠BCE=180°-145°

⇒∠BCE=35°

Now, as ∠BCE=35°  and ∠ABC=35°⇒BE=CE(Sides opposite to equal angles are always equal)

Hence proved.