Find adjacent corners if: 1) one of them is 17 times larger than the second; 2) their degree measures are related as 19: 26.

Let’s solve this problem using equations.
1) Let one of the adjacent angles be x degrees, then the second of the adjacent angles is 17 * x degrees. We know that the sum of the degree measures of adjacent angles is 180 degrees. Let’s make the equation:
x + 17 * x = 180;
x * (1 + 17) = 180;
x * 18 = 180;
x = 180: 18;
x = 10 degrees – one of the adjacent corners;
17 * 10 = 170 degrees – the second of the adjacent angles.
Answer: 10 and 170 degrees.
2) Let one of the adjacent angles be 19 * x degrees, then the second of the adjacent angles is 26 * x degrees. We know that the sum of the degree measures of adjacent angles is 180 degrees. Let’s make the equation:
19 * x + 26 * x = 180;
x * (19 + 26) = 180;
x * 45 = 180;
x = 180: 45;
x = 4 degrees;
19 * 4 = 76 degrees – one of the adjacent corners;
26 * 4 = 104 degrees – the second of the adjacent angles.
Answer: 76 and 104 degrees.