ABC IS A RIGHT TRIANGLE,RIGHT ANGLED AT B. THE BISECTOR OF A AND C MEET AT D. FIND ADC

Given : ABC is a right Δ, right angled at B and AD and CD are angle bisectors of ∠A and ∠C.

Now, in ΔABC,

∠A + ∠B + ∠C = 180°

⇒∠A + ∠C = 180° – ∠B = 180° – 90° = 90°  ......... (2)

In ΔADC,

∠ABC + ∠CAD + ∠ACD = 180°

⇒ ∠ADC = 180° – (∠CAD + ∠ACD)