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МатематикаВопрос:
4) In triangle ABC, angle C is 15°. Sides AC and BC are marked with equal dashes, indicating they are equal in length. Find the angle at vertex A.
Ответ:
Решение:
Треугольник, у которого две стороны равны, называется равнобедренным. В равнобедренном треугольнике углы, лежащие напротив равных сторон (углы при основании), также равны.
- Так как стороны AC и BC равны, то углы, лежащие напротив них (углы A и B), также равны.
- Сумма углов в треугольнике равна 180°.
- Обозначим угол A как x. Тогда угол B тоже равен x.
- Уравнение: x (угол A) + x (угол B) + 15° (угол C) = 180°.
- 2x + 15° = 180°.
- 2x = 180° - 15°.
- 2x = 165°.
- x = 165° / 2 = 82.5°.
Ответ: 82.5°
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- 2) One angle of a right-angled triangle is 45°. Find the other acute angle.
- 3) In an isosceles triangle, one of the base angles is 80°. Find the vertex angle.
- 5) In triangle ABC, sides AB and BC are equal. Angle ACD is 120°. Find the angles at A and B.
- 6) In triangle ABC, AB = BC. Angle CAD is marked with two arcs, and angle BAC is marked with one arc, suggesting they are equal. Angle C is 50°. Find the angle marked with a question mark.
- 7) In the figure ABCD, AB is parallel to CD, and AD is parallel to BC. The angle at vertex A is 137°, and the angle at vertex D is 0. This is likely a typo for a quadrilateral ABCD, where AB is parallel to CD and AD is parallel to BC, which makes it a parallelogram. In a parallelogram, opposite angles are equal and consecutive angles sum to 180°. If angle A is 137°, then angle C is also 137°. Angles B and D would be 180° - 137° = 43°. The notation '0' for angle D is incorrect. Assuming it's a parallelogram with ∠A = 137°.
