Question

in a quadrilateral ABCD AO and bo are the bisectors of angle C and angle D respectively prove that angle COD is equal to half of angle A + Angle B


Write it with fully detail plzzzzz​

Answer 1

according to alternate interior angles COD is quite opposite to angle A . diagnol must be bisecting them

Answer 2

Answer:

∠a + ∠b = 180°

1/2 (∠a + ∠b) = 90°

in tri. AOB, ∠oab + oba +∠aob = 180°

now, ∠aob + 90° = 180° (∵ ∠oab + ∠oba = 90° )

so ∠aob = 180° - 90° = 90°

now, ∠d + ∠c = 180°

so, 1/2 (∠d + ∠c) = 90°

therefore,∠aob = 1/2(∠d + ∠c) = 90°

hence, proved