Реши задачу

Углы \(CDE\) и \(FDE\) смежные. Угол \(CDE\) на \(24\degree\) меньше угла \(FDE\) . Вычисли градусные меры этих углов.

Решение.

1. Так как углы \(CDE\) и \(FDE\) [вертикальные|смежные] (по условию), то \(\angle CDE\) [ \(-\) | \(+\) | \(\cdot\) | \(\div\) ] \(\angle FDE =\) [ ] \(\degree\) (по [аксиоме|теореме|свойству][смежных|вертикальных] углов).

2. Так как угол \(CDE\) на \(24\degree\) [больше|меньше] угла \(FDE\) (по условию), то \(\angle\) [ \(CDE\) | \(FDE\) ] \( =\angle \) [ \(CDE\) | \(FDE\) ][ \(-\) | \(+\) | \(\cdot\) | \(\div\) ] \(24\degree\) .

3. Так как \(\angle CDE\) [ \(-\) | \(+\) | \(\cdot\) | \(\div\) ] \(\angle FDE =\) [ ] \(\degree\) (п. \(1\) ) и \(\angle\) [ \(CDE\) | \(FDE\) ] \(=\angle \) [ \(CDE\) | \(FDE\) ][ \(-\) | \(+\) | \(\cdot\) | \(\div\) ] \(24\degree\) (п. \(2\) ), то \(\angle\) [ \(C\) | \(F\) ] \(DE\) [ \(-\) | \(+\) | \(\cdot\) | \(\div\) ] \(\angle \) [ \(F\) | \(C\) ] \(DE\) [ \(-\) | \(+\) | \(\cdot\) | \(\div\) ][ ] \( \degree\) \(=\) [ ] \(\degree\) , тогда [ \(1\) | \(2\) | \(3\) | \(4\) ] \(\angle \) [ \(FDE\) | \(CDE\) ] \(=\) [ ] \(\degree\) .Следовательно, \(\angle \) [ \(CDE\) | \(FDE\) ] \(=\) [ ] \(\degree\) .

4. Так как \(\angle\) [ \(FDE\) | \(CDE\) ] \(=\) [ ] \(\degree\) (п. \(3\) ) и \(\angle\) [ \(CDE\) | \(FDE\) ] \(=\angle \) [ \(CDE\) | \(FDE\) ] \(+~24\degree\) (п. \(2\) ), то \(\angle \) [ \(FDE\) | \(CDE\) ] \(=\) [ ] \(\degree\) .

Ответ: \(\angle CDE\) равен [ ] \(\degree\) , \(\angle FDE\) равен [ ] \(\degree\) .