The sum of the vertical angles AOB and COD formed at the intersection of lines AD and BC is 130
| May 9, 2021 | education
The sum of the vertical angles AOB and COD formed at the intersection of lines AD and BC is 130 degrees. Find the angle BOD?
Given: lines AD and BC intersect at point O; corners AOB and COD – vertical; the sum of the angles AOB and COD is 130 °.
Find: Corner BOD.
Solution: the angles AOB and COD are vertical, therefore the angles AOB and COD are equal;
the sum of the angles AOB and COD is 130 °, the angles AOB and COD are equal, therefore, the angles AOB and COD are 130 °: 2 = 65 °;
the angles AOB and BOD are adjacent, the angle AOB is 65 °, therefore, the angle BOD is 180 ° – 65 ° = 115 °.
Answer: 115o.
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