1. The problem asks for the measure of each interior angle of a regular 19-gon. 2. The formula to find the measure of each interior angle of a regular polygon with $n$ sides is: $$\text{Each interior angle} = \frac{(n-2) \times 180^\circ}{n}$$ 3. For a 19-gon, substitute $n=19$: $$\text{Each interior angle} = \frac{(19-2) \times 180^\circ}{19} = \frac{17 \times 180^\circ}{19}$$ 4. Calculate the numerator: $$17 \times 180^\circ = 3060^\circ$$ 5. Now divide by 19: $$\frac{3060^\circ}{19}$$ 6. To simplify, write the division with cancellation: $$\frac{\cancel{3060^\circ}}{\cancel{19}}$$ (Here, no common factors to cancel, so proceed with division.) 7. Perform the division: $$3060 \div 19 = 161.0526315789^\circ$$ 8. Therefore, each interior angle of a regular 19-gon measures approximately: $$161.05^\circ$$ Final answer: Each interior angle of a regular 19-gon is approximately $161.05^\circ$.