Question

найдите большой угол равнобедреной трапеции АВСД,если диагональ АС образует с основанием АД и боковой стороной АВ углы ,равные 43 и 25 соответственно

Answer 1

Угол А = 43° + 25° = 68°
В равнобедренной трапеции противолежащие углы в сумме дают 180°:
Угол С = 180° - 68° = 112°
А еще в равнобедренной трапеции углы при основании равны:
Угол А = углу D
Угол С = углу В

Answer 2

Finding the measure of the larger angle in an isosceles trapezoid

To find the measure of the larger angle in an isosceles trapezoid ABCD, we need to use the given information about the angles formed by the diagonal AC with the base AD and the side AB.

Let's denote the measure of the larger angle as x.

According to the given information, the angle formed by the diagonal AC with the base AD is 43 degrees, and the angle formed by the diagonal AC with the side AB is 25 degrees.

To find the measure of the larger angle x, we can use the fact that the sum of the interior angles of a trapezoid is equal to 360 degrees.

In an isosceles trapezoid, the base angles (angles formed by the bases AD and BC) are congruent. Therefore, we can write the equation:

x + x + 43 + 25 = 360

Simplifying the equation:

2x + 68 = 360

Subtracting 68 from both sides:

2x = 292

Dividing both sides by 2:

x = 146

Therefore, the measure of the larger angle in the isosceles trapezoid ABCD is 146 degrees.