In the adjoining diagram, state whether ABC is a straight line or not when `x= (8)/(9)` right angle and `y= 100^(@)`

Answer

To determine whether ABC is a straight line given the angles \( x \) and \( y \), we can follow these steps:

### Step 1: Understand the given angles
We are given:
- \( x = \frac{8}{9} \) of a right angle
- \( y = 100^\circ \)

### Step 2: Convert \( x \) to degrees
A right angle is \( 90^\circ \). Therefore, we can calculate \( x \) as follows:
\[ x = \frac{8}{9} \times 90^\circ \]

### Step 3: Calculate \( x \)
Now, let's perform the multiplication:
\[ x = \frac{8 \times 90}{9} = \frac{720}{9} = 80^\circ \]

### Step 4: Add the angles \( x \) and \( y \)
Now that we have \( x \), we can find the sum of \( x \) and \( y \):
\[ x + y = 80^\circ + 100^\circ \]

### Step 5: Calculate the sum
Perform the addition:
\[ x + y = 180^\circ \]

### Step 6: Determine if ABC is a straight line
Since the sum of angles \( x \) and \( y \) equals \( 180^\circ \), we conclude that:
- If \( x + y = 180^\circ \), then line ABC is a straight line.

### Final Conclusion
Thus, ABC is indeed a straight line.

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