Question

OC and OD are the bisectors of angle BCD and angle ADC respectively. If
angle ADC=70° and angle BCD=60°, find the measures of angle DOC and angle ABC.

Answer 1

Answer:

Given: In the given figure, AB || CD and O is the midpoint of AD.

To prove:

(i) ΔAOB ≅ ΔDOC.

(ii) O is the midpoint of BC.

Proof:

(i) In ΔAOB and ΔDOC,

∠BAO = ∠CDO                    (Alternate interior angles, AB || CD)

AO = DO                              (Given, O is the midpoint of AD)

∠AOB = ∠DOC                   (Vertically opposite angles)

 

∴ By ASA congruence criteria,

ΔAOB ≅ ΔDOC

(ii) ∵ ΔAOB ≅ ΔDOC           [From (i)]

∴ BO = CO                           (CPCT)

Hence, O is the midpoint of BC.

Step-by-step explanation:

Answer 2

Answer:

in triangle OCD the sum of all angles is 180 degree two angle BOC is 115 degree an angle abc is 120 degree because in quadrilateral opposite angles are supplementary