In the given figure , if a= b = c then `angle AOC =` ______ ??

Answer

To solve the problem, we need to find the value of angle AOC given that angles A, B, and C are equal (a = b = c). Here’s a step-by-step solution:

### Step 1: Understand the relationship between the angles
We know that angles A, B, and C are equal. Therefore, we can denote them as:
- Angle A = a
- Angle B = a
- Angle C = a

### Step 2: Use the property of angles
From the problem, we also know that the sum of angles A, B, and C is equal to 90 degrees because the lines OD and AO are perpendicular to each other. Thus, we can write:
\[ \text{Angle A} + \text{Angle B} + \text{Angle C} = 90^\circ \]
Substituting the values we have:
\[ a + a + a = 90^\circ \]
This simplifies to:
\[ 3a = 90^\circ \]

### Step 3: Solve for angle A
To find the value of angle A, we divide both sides of the equation by 3:
\[ a = \frac{90^\circ}{3} = 30^\circ \]
Thus, we have:
- Angle A = 30 degrees
- Angle B = 30 degrees
- Angle C = 30 degrees

### Step 4: Find angle AOC
Now, we need to find angle AOC, which is the sum of angles A and B:
\[ \text{Angle AOC} = \text{Angle A} + \text{Angle B} \]
Substituting the values we found:
\[ \text{Angle AOC} = 30^\circ + 30^\circ = 60^\circ \]

### Final Answer
Therefore, the value of angle AOC is:
\[ \text{Angle AOC} = 60^\circ \]

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