Question

Луч OC делит развернутый угол AOC на два смежных угла AOC и BOC так, что угол AOC на 30º больше угла BOC. Найдите < AOC и < BOC .

Answer 1

Так как развернутый угол равен 180 градусов, то АОВ+СОВ=180
пусть СОВ=х, то АОС=х+30
тогда х+х+30=180
х=75
тогда СОВ=75
АОС=75+30=105
Ответ. 75, 105.

Answer 2

Problem Analysis

We are given that angle AOC is divided into two adjacent angles, AOC and BOC, in such a way that angle AOC is 30º larger than angle BOC. We need to find the measures of angles AOC and BOC.

Solution

Let's assume the measure of angle BOC is xº. According to the given information, angle AOC is 30º larger than angle BOC, so the measure of angle AOC is (x + 30)º.

Since the sum of the measures of angles in a triangle is 180º, we can write the equation:

x + (x + 30) + 180 = 180

Simplifying the equation, we get:

2x + 30 = 0

Subtracting 30 from both sides, we have:

2x = -30

Dividing both sides by 2, we get:

x = -15

Since angles cannot have negative measures, we can conclude that angle BOC does not have a valid measure.

Therefore, there is no valid solution for the measures of angles AOC and BOC that satisfy the given conditions.

Conclusion

The problem does not have a valid solution for the measures of angles AOC and BOC that satisfy the given conditions.