Question

сумма углов А и В трапеции АВСD в три раза больше угла С.Найдите угол D ответ в градусах

Answer 1

Сумма углов трапеции = 360 град., значит A+B+C+D = 360

A+B = 3C (по условию)

углы C и D односторонние, а значит их сумма = 180 град   => C = 180-D

Подставим 2 последних условия в первое:

3(180-D) + 180 - D = 360

Решаем уравнение:

3D = 360

D = 120 

 

Answer 2

Calculation of Angle D in Trapezoid ABCD

To find the measure of angle D in trapezoid ABCD, we are given that the sum of angles A and B is three times the measure of angle C, and we need to determine the measure of angle D in degrees.

Let's denote the measure of angle C as x. According to the given information, the sum of angles A and B is three times the measure of angle C, which can be expressed as:

A + B = 3x In a trapezoid, the sum of the interior angles is equal to 360 degrees. Therefore, we can write the equation:

A + B + C + D = 360 Substituting the value of A + B from the first equation into the second equation, we get:

3x + C + D = 360

Since we know that the sum of angles A and B is three times the measure of angle C, we can substitute 3x for A + B:

3x + C + D = 360

Now, we need to isolate the measure of angle D. Rearranging the equation, we have:

D = 360 - 3x - C

To find the measure of angle D in degrees, we need to substitute the value of x and C into the equation. Unfortunately, the provided search results do not contain the specific values of x and C for this trapezoid. Therefore, without the specific values, we cannot calculate the measure of angle D.

Please provide the specific values of angle C or any additional information to proceed with the calculation.