The sum of 3 distinct angles is equal to the sum of 2 right angles and the difference between two pairs of the angles is `10^(@)`. Find the smallest among the angles.

Answer

To solve the problem step by step, we will follow the reasoning laid out in the video transcript.

### Step 1: Define the angles
Let the smallest angle be \( x \) degrees. According to the problem, we have three distinct angles.

### Step 2: Express the other angles
Since the difference between two pairs of angles is \( 10^\circ \):
- The second angle can be expressed as \( x + 10 \) degrees.
- The third angle can be expressed as \( x + 20 \) degrees.

### Step 3: Set up the equation
The sum of the three angles is equal to the sum of two right angles, which is \( 180^\circ \). Therefore, we can write the equation:
\[ x + (x + 10) + (x + 20) = 180 \]

### Step 4: Simplify the equation
Now, simplify the left side of the equation:
\[ x + x + 10 + x + 20 = 180 \]
This simplifies to:
\[ 3x + 30 = 180 \]

### Step 5: Solve for \( x \)
Next, we will isolate \( x \):
\[ 3x = 180 - 30 \]
\[ 3x = 150 \]
Now, divide both sides by 3:
\[ x = \frac{150}{3} = 50 \]

### Step 6: Identify the smallest angle
The smallest angle is \( x \), which we found to be \( 50^\circ \).

### Final Answer
The smallest angle among the three distinct angles is \( 50^\circ \).

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