Question

AOB = 90°. найдите AOC и ВОС​

Answer 1

Ответ:

а)

$3x - 5 + x + 15 = 90 \\ 4x = 90 - 1 0\\ 4x = 80 \\ x = 20 \\\\ \angle AOC = 3 \times 20^{\circ} - 5^{\circ} = 55^{\circ} \\\angle \: BOC = 20^{\circ} + 15^{\circ} = 35^{\circ}$

б)

$4x + 30 + x = 90 \\ 5x = 90 - 30 \\ 5x = 60 \\ x = 12 \\ \\ \angle BOC = 4 \times 12^{\circ} + 30^{\circ} = 48^{\circ} + 30^{\circ} =78^{\circ} \\ \angle \: AOC = 12^{\circ}$

в)

$3x - 35 + 2x + 25 = 90 \\ 5x = 90 + 10 \\ 5x = 100 \\ x = 20 \\ \\ \angle AOC = 2 \times 20^{\circ} + 25 ^{\circ} = 65^{\circ} \\ \angle \: BOC= 3 \times 20^{\circ} - 35^{\circ} = 25^{\circ}$