Line segments AB and CD intersect at point O. Ray OK is the bisector of angle DOB. Find DOK angle

Line segments AB and CD intersect at point O. Ray OK is the bisector of angle DOB. Find DOK angle if AOD angle = 84 degrees?

Given:

AD ∩ ВС = O

OK – bisector of angle DOB

Angle AOD = 84 °

To find :

DOK angle

Solution :

The angles AOD and DOB are adjacent, which means their sum is 180,

∠AOD + ∠DOB = 180 ° (adjacent corners)

=> ∠DOB = 180 – ∠AOD = 180 ° – 84 ° = 96 °

∠DOK = 1/2 ∠DOB (ОK – bisector ∠DOB)

∠DOK = 96 ° / 2 = 48 °

Answer: ∠DOK = 48 °