The sum of the vertical angles KON and COD, formed at the intersection of the straight

The sum of the vertical angles KON and COD, formed at the intersection of the straight lines KD and NC, is equal to 116 °. Find the corner NOD.

1. Considering that the vertical angles are equal (according to their properties), and their sum is equal to 116 ° according to the problem statement, we calculate their value:

∠KON = ∠СОD = 116 °: 2 = 58 °.

2. Considering that ∠∠KON and ∠СOK are adjacent angles, and their total value is 180 °, we calculate the degree measure ∠СOK:

∠SOK = 180 ° – ∠KON = 180 ° – 58 ° = 122 °.

3. ∠KOS = ∠DON, since they are vertical. ∠BOD = 122 °.

Answer: ∠DON is equal to 122 °.