Question

in given figure prove that angle ADC is equal to angle A + Angle B + angle C

Answer 1

Answer is in the attachment below

Answer 2

Answer:

The proof is explained below.

Step-by-step explanation:

In the given figure ABCD, we have to prove that

∠A+∠B+∠C=∠ADC

Let us do construction: Join BD

In ΔABD,

By exterior angle property which states that an exterior angle of triangle is equal to the sum of opposite interior angles i.e

∠1+∠2=∠5  →    (1)

Similarly in ΔCBD

∠4+∠3=∠6  →    (2)

Adding equation (1)a nd (2), we get

∠1+∠2+∠4+∠3= ∠5 +∠6

⇒ ∠1+(∠2+∠3)+∠4=∠ADC

⇒ ∠A+∠B+∠C=∠ADC

Hence proved.