Question

высот равнобедренной трапеции проведенная из вершины острого угла,образует с боковой стороной угол 24 градуса.найдите углы трапеции

Answer 1

Так как угол А в треугольнике ADH =24гр., то угол А в трапеции ABDC=24+90=114гр.

следовательно угол D равен 180-114=66гр.

А так как трапеция р\б => угол А=углу В, а угол D=углу С. 

Answer 2

Finding the Angles of an Isosceles Trapezoid

To find the angles of an isosceles trapezoid, we are given that a height drawn from the vertex of the acute angle forms a 24-degree angle with one of the lateral sides.

Let's denote the acute angle as A, the base angles as B and C, and the obtuse angle as D.

To find the angles, we can use the fact that the sum of the angles in a trapezoid is 360 degrees.

Solution:

1. We know that the sum of the angles in a trapezoid is 360 degrees. 2. Let's denote the acute angle as A and the base angles as B and C. 3. We are given that the height drawn from the vertex of angle A forms a 24-degree angle with one of the lateral sides. 4. Since the trapezoid is isosceles, the base angles B and C are equal. 5. Let's set up an equation to find the value of angle A: - Angle A + Angle B + Angle C + Angle D = 360 degrees. - Angle A + Angle B + Angle B + Angle D = 360 degrees. (Substituting C with B since they are equal) - Angle A + 2 * Angle B + Angle D = 360 degrees. 6. We are given that the height forms a 24-degree angle with one of the lateral sides. This means that Angle B is 24 degrees. 7. Substituting the value of Angle B into the equation, we get: - Angle A + 2 * 24 degrees + Angle D = 360 degrees. - Angle A + 48 degrees + Angle D = 360 degrees. - Angle A + Angle D = 360 degrees - 48 degrees. - Angle A + Angle D = 312 degrees. 8. Since the sum of the angles A and D is 312 degrees, we cannot determine the exact values of angles A and D without additional information.

In conclusion, we can determine that the sum of angles A and D in the isosceles trapezoid is 312 degrees, but we cannot determine the exact values of these angles without additional information.

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