Question

Прямые АD и ВС пересекаются в точке О. сумма вертикальных углов АОВ и СОD равна 108 градусам. найти все 4 угла

Answer 1

Сумма вертикального и смежного угла равна 180°, зн. угол ВОD = 180-108=72°.
Смежные углы равны, зн. угол AOC=BOD=72°
Ответ : АОВ и СОD = 108°
AOC и BOD=72°

Answer 2

Given Information:

We are given that lines AD and BC intersect at point O, and the sum of vertical angles AOV and COD is equal to 108 degrees.

Solution:

To find all four angles, we need to determine the measures of angles AOV, COD, AOD, and COB.

Let's start by finding the measure of angle AOV. Since vertical angles are congruent, angle AOV is equal to angle COD. Therefore, the measure of angle AOV is 108/2 = 54 degrees.

Next, we can find the measure of angle COD, which is also 54 degrees.

Now, let's find the measure of angle AOD. Angle AOD is a straight angle, which measures 180 degrees. Since angle AOV is 54 degrees, we can subtract that from 180 to find the measure of angle AOD: 180 - 54 = 126 degrees.

Finally, we can find the measure of angle COB. Angle COB is also a straight angle, so it measures 180 degrees. Since angle COD is 54 degrees, we can subtract that from 180 to find the measure of angle COB: 180 - 54 = 126 degrees.

To summarize: - Angle AOV = 54 degrees - Angle COD = 54 degrees - Angle AOD = 126 degrees - Angle COB = 126 degrees

Please let me know if there's anything else I can help you with!