Вправи: 573

573. ∠BCD — зовнішній кут ∆АВС. Заповніть таблицю 21.

1) ∠С = 180° – (∠А + ∠В) = 180° – (35° + 55°) = 180° – 90° = 90°; ∠BCD = ∠A + ∠B = 35° + 55° = 90°;

2) ∠A = 180° – (∠B + ∠C) = 180° – (45° + 45°) = 180° – 90° = 90°; ∠BCD = ∠A + ∠B = 90° + 45° = 135°;

3) ∠B = 180° – (∠A + ∠C) = 180° – (20° + 65°) = 180° – 85° = 95°; ∠BCD = ∠A + ∠B = 20° + 95° = 115°;

4) ∠BCD = ∠A + ∠B;∠A = ∠BCD – ∠B = 60° – 30° = 30°; ∠C = 180° –

– (∠A + ∠B) = 180° – (30° + 30°) = 180° – 60° = 120°.

∠A	35°	90°	20°	30°
∠B	55°	45°	95°	30°
∠C	90°	45°	65°	120°
∠BCD	90°	135°	115°	60°