Question

Как решить задачу? угол NOK равен 120°, OD-луч,проведеный внури него. скрлько градусов содержит угол DOK,если градусная мера угла NOD:в 2 раза меньше градусной меры угла DOK? даю 20 балов!задачу надо решить уравнением!

Answer 1

Пусть угол NOD будет х градусов, тогда DOК будет 2х - он в 2 раза больше
в итоге х+2х=120
3х=120
х=120:3
х=40
2х=2*40=80 - угол DOК
Ответ: 80 градусов

Answer 2

Problem Analysis

We are given that the angle NOK is equal to 120° and that OD is a ray drawn inside this angle. We need to find the measure of angle DOK if the measure of angle NOD is twice the measure of angle DOK.

Solution

Let's assume the measure of angle DOK is x. According to the problem, the measure of angle NOD is twice the measure of angle DOK, so the measure of angle NOD is 2x.

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

x + 2x + 120° = 180°

Simplifying the equation:

3x + 120° = 180°

Subtracting 120° from both sides:

3x = 60°

Dividing both sides by 3:

x = 20°

Therefore, the measure of angle DOK is 20°.

Answer

The measure of angle DOK is 20°.