4. Дано: \(\angle\) ABD = 100°, \(\angle\) CBD = 4 \(\cdot\) \(\angle\) ABC. Найти: \(\angle\) ABC и \(\angle\) CBD.

Решение:

1. Пусть \( \angle ABC = x \). Тогда \( \angle CBD = 4x \).
2. \( \angle ABD = \angle ABC + \angle CBD \)
3. \( 100° = x + 4x \)
4. \( 100° = 5x \)
5. \( x = 20° \)
6. \( \angle ABC = 20° \)
7. \( \angle CBD = 4 \cdot 20° = 80° \)

Ответ: \( \angle ABC = 20°, \angle CBD = 80° \).