Question

In the parallelogram given below, find the measures of ∠ABO and ∠ACB. ​

Answer 1

Solution:-

➡️In the parallelogram given above ∠AOB and ∠COD are vertically opposite angles.

➡️Because vertically opposite angles are equal, we have 

∠AOB  =  ∠COD

∠AOB  =  105°

➡️In triangle ABO, we have

∠OAB + ∠AOB + ∠ABO  =  180°

➡️Plug ∠OAB  =  30° and ∠AOB  =  105°.

30° + 105° + ∠ABO  =  180°

135° + ∠ABO  =  180°

∠ABO  =  45°

➡️In the parallelogram given above, AD||BC, AC is transversal and  ∠OCB and ∠OAD are alternate interior angles.

If two parallel lines are cut by a transversal, alternate interior angles are equal. 

So, we have 

∠OCB  =  ∠OAD

➡️In the parallelogram given above, ∠OAD  =  45°.

So, we have 

∠OCB  =  45°

➡️Because ∠OCB  ≅ ∠ACB, we have

∠ACB  =  45°

➡️Hence, the measures of ∠ABO and ∠ACB are 45° each.

Answer 2

Answer:

angle ABO=45 angel ACB = 45