Question

Градусна міра кута COD дорівнює 120º. Промінь ОМ проходить між сторонами заданого кута так, що кут СОМ утричі менший за кут MOD. Знайти градусну міру більшого з утворених кутів.​

Answer 1

Градусна міра кута COD дорівнює 120º. Промінь ОМ проходить між сторонами заданого кута так, що кут СОМ утричі менший за кут MOD. Знайти градусну міру більшого з утворених кутів.

Understanding the problem

To solve this problem, we need to find the measure of the larger of the two angles formed by the ray OM and the sides of the given angle COD. We are given that the measure of angle COD is 120º, and that angle COM is one-third the size of angle MOD.

Solution

Let's assume that the measure of angle COM is x degrees. Since angle COM is one-third the size of angle MOD, we can write the equation:

x = (1/3) * (180 - 120)

Simplifying the equation, we have:

x = (1/3) * 60 x = 20

Therefore, the measure of angle COM is 20 degrees. Since angle COM is smaller than angle MOD, we can find the measure of angle MOD by subtracting the measure of angle COM from the measure of angle COD:

Measure of angle MOD = Measure of angle COD - Measure of angle COM Measure of angle MOD = 120 - 20 Measure of angle MOD = 100 degrees

So, the measure of the larger of the two angles formed is 100 degrees.

Conclusion

The measure of the larger of the two angles formed by the ray OM and the sides of the given angle COD is 100 degrees.