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ГДЗ Геометрія 7 клас Бурда
Роздiл 4. Трикутники
У трикутнику ABC проведено бісектриси AK, BM i CN. Знайдіть кути BAK, CAK, ACN, BCN, ABM, CBM, якщо: 1) ∠A= 130°, ∠B = 20°, ∠C = 30°; 2) ∠A= 70°, ∠B = ∠C= 55°; 3) ∠A = 40°, ∠B = 90°, ∠C = 50°; 4) ∠A= ∠B = ∠C= 60°.
1) ∠BAK = ∠CAK = 1/2 ∠A = 1/2 • 130° = 65°, ∠CAN = ∠BCN = 1/2 ∠C = 1/2 • 30° = 15°, ∠ABM = ∠CBM = 1/2 ∠B = 1/2 • 20° = 10°;
2) ∠BAK = ∠CAK = 1/2 ∠A = 1/2 • 70° = 35°, ∠CAN = ∠BCN = 1/2 ∠C = 1/2 • • 55° = 27°30’, ∠ABM = ∠CBM = 1/2 ∠B = 1/2 • 55° = 27°30’;
3) ∠BAK = ∠CAK = 1/2 ∠A = 1/2 • 40° = 20°, ∠CAN = ∠BCN = 1/2 ∠C = = 1/2 • 50° = 25°, ∠ABM = ∠CBM = 1/2 ∠B = 1/2 • 90° = 45°;
4) ∠BAK = ∠CAK = 1/2 ∠A = 1/2 • 60° = 30°, ∠CAN = ∠BCN = 1/2 ∠C = 1/2 • • 60° = 30°, ∠ABM = ∠CBM = 1/2 ∠B = 1/2 • 60° = 30°.
1) ∠BAK = ∠CAK = 1/2 ∠A = 1/2 • 130° = 65°, ∠CAN = ∠BCN = 1/2 ∠C = 1/2 • 30° = 15°, ∠ABM = ∠CBM = 1/2 ∠B = 1/2 • 20° = 10°;
2) ∠BAK = ∠CAK = 1/2 ∠A = 1/2 • 70° = 35°, ∠CAN = ∠BCN = 1/2 ∠C = 1/2 • • 55° = 27°30’, ∠ABM = ∠CBM = 1/2 ∠B = 1/2 • 55° = 27°30’;
3) ∠BAK = ∠CAK = 1/2 ∠A = 1/2 • 40° = 20°, ∠CAN = ∠BCN = 1/2 ∠C = = 1/2 • 50° = 25°, ∠ABM = ∠CBM = 1/2 ∠B = 1/2 • 90° = 45°;
4) ∠BAK = ∠CAK = 1/2 ∠A = 1/2 • 60° = 30°, ∠CAN = ∠BCN = 1/2 ∠C = 1/2 • • 60° = 30°, ∠ABM = ∠CBM = 1/2 ∠B = 1/2 • 60° = 30°.