Line segments AB and CD intersect at point O. Ray OK is the bisector of angle DOB. Find DOK angle
July 24, 2021 | education
| 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 °
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