Three angles of aquadrilateral are respectively `90^(@),91^(@),69^(@).` Find the fourth angle.

Answer

To find the fourth angle of the quadrilateral when three angles are given, we can follow these steps:

### Step 1: Understand the properties of a quadrilateral
The sum of all interior angles in a quadrilateral is always 360 degrees.

### Step 2: Write down the known angles
The given angles are:
- Angle A = 90°
- Angle B = 91°
- Angle C = 69°

### Step 3: Set up the equation
Let the fourth angle be represented as \( X \). According to the property of quadrilaterals, we can write the equation:
\[ \text{Angle A} + \text{Angle B} + \text{Angle C} + \text{Angle D} = 360° \]
Substituting the known values:
\[ 90° + 91° + 69° + X = 360° \]

### Step 4: Simplify the equation
Now, we can add the known angles together:
\[ 90 + 91 = 181 \]
\[ 181 + 69 = 250 \]
So, we can rewrite the equation as:
\[ 250° + X = 360° \]

### Step 5: Solve for \( X \)
To find \( X \), subtract 250° from both sides of the equation:
\[ X = 360° - 250° \]
\[ X = 110° \]

### Step 6: Conclusion
Thus, the fourth angle \( D \) is:
\[ \text{Angle D} = 110° \]

### Final Answer
The fourth angle of the quadrilateral is \( 110° \).

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