Question

Луч ос лежит внутри угла AOB равного 60 градусов Найдите угол AOC если он на 30 градусов больше угла BOC

Answer 1

Пусть AOC=a - альфа
AOB=a+(a-30°)
a+(a-30°)=60°
2a-30°=60°
2a=90°
a=45°
Ответ: 45

Answer 2

Problem Analysis

We are given that angle AOB is equal to 60 degrees, and we need to find angle AOC, which is 30 degrees larger than angle BOC.

Solution

To find angle AOC, we can use the fact that the sum of angles in a triangle is 180 degrees. We can start by finding angle BOC using the given information.

Let's assume angle BOC is x degrees. Then, angle AOC is x + 30 degrees.

Since angle AOB is equal to 60 degrees, we can write the equation:

angle AOB + angle BOC + angle AOC = 180 degrees

Substituting the given values, we get:

60 + x + (x + 30) = 180

Simplifying the equation:

2x + 90 = 180

Subtracting 90 from both sides:

2x = 90

Dividing both sides by 2:

x = 45

Therefore, angle BOC is 45 degrees.

Now, we can find angle AOC:

angle AOC = angle BOC + 30 = 45 + 30 = 75 degrees.

So, angle AOC is 75 degrees.

Answer

The angle AOC is 75 degrees.