Question

Луч OC делит развёрнутый угол AOB на два смежных угла AOC иBOC так , что угол AOC в 3 раза больше угла BOC. Найдите AOC и BOC

Answer 1

развернутый угол= 180 градусам

х+50( угол АОС) + х( второй угол) = 180

2х=180-50

2х=130

х=65 градусов ( угол ВОС)

угол АОС=65+50 = 115 градусов

Ответ: 65 градусов и 115 градусов

Answer 2

Problem Statement

Дан развёрнутый угол AOB, который делит на два смежных угла AOC и BOC так, что угол AOC в 3 раза больше угла BOC. Найдите значения углов AOC и BOC.

Solution

Let's assume the measure of angle BOC is x degrees. Since angle AOC is 3 times larger than angle BOC, the measure of angle AOC will be 3x degrees.

According to the problem statement, the sum of angles AOC and BOC should be equal to the measure of angle AOB. Since angle AOB is a straight angle (180 degrees), we can write the following equation:

AOC + BOC = AOB

Substituting the values we have:

3x + x = 180

Simplifying the equation:

4x = 180

Dividing both sides by 4:

x = 45

Therefore, the measure of angle BOC is 45 degrees, and the measure of angle AOC is 3 times larger, which is 3 * 45 = 135 degrees.

So, the values of angles AOC and BOC are 135 degrees and 45 degrees, respectively.

Answer: Angle AOC = 135 degrees Angle BOC = 45 degrees