Find adjacent corners if one of them is 17 times the other.

1. Let us denote the degree measure of the smaller of the adjacent angles by x.

2. Define the degree measure of the larger angle:

17 * x = 14x.

3. Since the sum of adjacent angles is equal to 180˚, compose and solve the equation:

17x + x = 180˚;

18x = 180˚;

x = 180˚: 18;

x = 10˚.

4. The degree measure of the smaller of the adjacent angles is x = 10˚.

5. What is the degree measure of the larger angle?

17 * x = 17 * 10˚ = 170˚.

Answer: The degree of the smaller angle is 10˚, the degree of the larger angle is 170˚.