Question

Диагонали прямоугольника abcd пересекаются в точке о. Найдите угол adb если он на 135 градусов меньше угла boc.

Answer 1

Смотри угол всo = аod тк они вертикальные 
Углы А и D в треугольнике AOD равны тк он равнобедренный( диогонали прямоугольника точкой пересечения делются пополам следовательно они равны)
Пусть угол ODA- x тогда AOD - 135 x
Значит x+x+135+x=180
3x+135=180
3x=45
x=15
ответ 15

Answer 2

Finding the Angle ADB in a Rectangle ABCD

To find the angle ADB in a rectangle ABCD, we need to use the information given in the question: the diagonals of the rectangle intersect at point O, and the angle ADB is 135 degrees less than the angle BOC.

Let's break down the problem step by step:

1. We know that the diagonals of a rectangle bisect each other. This means that point O is the midpoint of both diagonals AC and BD.

2. Since O is the midpoint of AC, we can say that AO = CO and BO = DO.

3. Now, let's consider the angle BOC. Since O is the midpoint of AC, we can draw a line segment from O to the midpoint of BC, which we'll call M. This line segment OM will be half the length of AC.

4. From the given information, we know that the angle ADB is 135 degrees less than the angle BOC. So, we can express the angle ADB as BOC - 135 degrees.

5. To find the angle BOC, we need to use the properties of a rectangle. In a rectangle, opposite angles are equal, so angle ABC is equal to angle ADC.

6. Since angle ABC is equal to angle ADC, we can say that angle BOC is equal to 2 times angle ABC (or 2 times angle ADC).

7. To find angle ABC (or ADC), we can use the fact that the sum of the angles in a triangle is 180 degrees. In triangle ABC (or ADC), we have angle ABC (or ADC), angle BAC (or DAC), and angle BCA (or DCA). Since it's a rectangle, angle BAC (or DAC) is 90 degrees.

8. Using the fact that the sum of the angles in a triangle is 180 degrees, we can find angle ABC (or ADC) by subtracting 90 degrees from 180 degrees and then dividing the result by 2.

9. Once we have angle ABC (or ADC), we can find angle BOC by multiplying it by 2.

10. Finally, we can find angle ADB by subtracting 135 degrees from angle BOC.

Let's summarize the steps:

1. Find the measure of angle ABC (or ADC) by subtracting 90 degrees from 180 degrees and dividing the result by 2. 2. Find the measure of angle BOC by multiplying angle ABC (or ADC) by 2. 3. Find the measure of angle ADB by subtracting 135 degrees from angle BOC.

Please note that without the specific measurements of the angles or the lengths of the sides of the rectangle, we cannot provide an exact numerical answer. However, the steps outlined above should help you find the measure of angle ADB based on the given information.

Note: The specific sources provided did not contain the exact information needed to answer the question. However, the steps outlined above are based on the properties of rectangles and the given information in the question.