Question

Бічна сторона рівнобічної трапеції дорівнює більшій основі , а діагональ трапеції утворює з основою кут 48 градусів. Знайдіть кути трапеції

Answer 1

Ответ:

48°   48°    84°

Объяснение:

Answer 2

The angles of a trapezoid can be found using the given information:

To find the angles of a trapezoid, we can use the fact that the sum of the interior angles of any quadrilateral is always equal to 360 degrees.

Let's denote the angles of the trapezoid as follows: - Angle A: the angle formed by the longer base and one of the legs - Angle B: the angle formed by the shorter base and one of the legs - Angle C: the angle formed by the longer base and the diagonal - Angle D: the angle formed by the shorter base and the diagonal

Since the trapezoid is isosceles, we know that angles A and B are congruent. Similarly, angles C and D are congruent.

We are given that the diagonal of the trapezoid forms a 48-degree angle with the longer base. Let's denote this angle as angle C.

Using the fact that the sum of the interior angles of a quadrilateral is 360 degrees, we can set up the following equation:

Angle A + Angle B + Angle C + Angle D = 360 degrees

Since angles A and B are congruent, and angles C and D are congruent, we can rewrite the equation as:

2 * Angle A + 2 * Angle C = 360 degrees

Simplifying the equation, we have:

Angle A + Angle C = 180 degrees

We are also given that angle C is 48 degrees. Substituting this value into the equation, we have:

Angle A + 48 degrees = 180 degrees

Solving for Angle A, we subtract 48 degrees from both sides:

Angle A = 180 degrees - 48 degrees Angle A = 132 degrees

Since angles A and B are congruent, we know that Angle B is also 132 degrees.

Therefore, the angles of the trapezoid are as follows: - Angle A = 132 degrees - Angle B = 132 degrees - Angle C = 48 degrees - Angle D = 48 degrees

I hope this helps! Let me know if you have any further questions.