In eqadrilateral ABCD, `angleA=100^(@),angleB=70^(@)andangleC:angleD=8:11,"then fine"angleD.`

Answer

To find angle D in quadrilateral ABCD where angle A = 100°, angle B = 70°, and the ratio of angle C to angle D is 8:11, we can follow these steps:

### Step 1: Write down the known angles and the ratio.
We know:
- Angle A = 100°
- Angle B = 70°
- The ratio of angle C to angle D is 8:11.

### Step 2: Express angle C in terms of angle D.
From the ratio, we can express angle C as:
\[ \text{angle C} = \frac{8}{11} \times \text{angle D} \]

### Step 3: Use the angle sum property of quadrilaterals.
The sum of the interior angles of a quadrilateral is 360°. Therefore, we can write:
\[ \text{angle A} + \text{angle B} + \text{angle C} + \text{angle D} = 360° \]

Substituting the known values:
\[ 100° + 70° + \left(\frac{8}{11} \times \text{angle D}\right) + \text{angle D} = 360° \]

### Step 4: Simplify the equation.
Combine the known angles:
\[ 170° + \left(\frac{8}{11} \times \text{angle D} + \text{angle D}\right) = 360° \]

Now, express angle D as a fraction:
\[ \text{angle D} = \frac{11}{11} \times \text{angle D} \]
Thus, we have:
\[ 170° + \left(\frac{8}{11} + \frac{11}{11}\right) \text{angle D} = 360° \]

Combine the fractions:
\[ 170° + \left(\frac{19}{11}\right) \text{angle D} = 360° \]

### Step 5: Isolate angle D.
Subtract 170° from both sides:
\[ \left(\frac{19}{11}\right) \text{angle D} = 360° - 170° \]
\[ \left(\frac{19}{11}\right) \text{angle D} = 190° \]

### Step 6: Solve for angle D.
Multiply both sides by the reciprocal of \(\frac{19}{11}\):
\[ \text{angle D} = 190° \times \frac{11}{19} \]

### Step 7: Calculate angle D.
Now, perform the multiplication:
\[ \text{angle D} = \frac{190 \times 11}{19} \]
Calculating \(190 \div 19\) gives \(10\):
\[ \text{angle D} = 10 \times 11 = 110° \]

### Conclusion:
Thus, the measure of angle D is:
\[ \text{angle D} = 110° \]