Question

if CD is a perpendicular to A B and C E bisector angle ACB find DCE

Answer 1

It is given that, CE bisect angle ∠ACB.

Therefore, ∠ACE = ∠ACB/2 -----(1)

In triangle ABC, ∠CAB + ∠ABC + ∠ACB = 180° ...[Since the sum of all three angles of a triangle is 180°]

⇒ 50° + 30° + ∠ACB = 180°

⇒ 80° + ∠ACB = 180°

⇒ ∠ACB = 180° - 80°

⇒ ∠ACB = 100°

⇒ ∠ACB/2 = 100/2

⇒ ∠ACE = 50° ...[From equation (1)]

Now in triangle ADC, ∠CAD + ∠ADC + ∠DCA = 180°

⇒ 50° + 90° + ∠DCA = 180°

⇒ ∠DCA = 180° - 90° - 50°

⇒ ∠DCA = 40°

Now,

 ∠DCE = ∠ACE - ∠DCA

⇒ ∠DCE = 50° - 40°

⇒ ∠DCE = 10°

Hence, the value of angle ∠DCE is 10°.

Answer 2

Answer:- Hope it will help you ;)