The sum of the vertical angles XOE and DOC formed at the intersection of lines XC and DE is 76 degrees. Find XOD.
| March 10, 2021 | education
1. Considering that the vertical angles are equal (according to their properties), and their sum is equal to 76 ° in
the condition of the problem, we calculate their value:
∠ХЕ = ∠SOD = 76 °: 2 = 38 °.
2. Taking into account that ∠XOE and DOC are adjacent angles, and their total value is
180 °, we calculate the degree measure ∠DOC:
∠DOC = 180 ° – ∠XOE = 180 ° – 38 ° = 142 °.
Answer: DOH is 142 °.
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