From the condition it is known that the values of adjacent angles are proportional to the numbers 5 and 7. And we need to find what is the difference between these angles.
Let us apply the theorem on the sum of adjacent angles to solve the problem. So, the sum of adjacent angles is 180 °.
Since we know how the angles are related we can write them as 5x and 7x.
We write down the sum of the angles and equate to 180 °.
5x + 7x = 180.
12x = 180;
x = 15.
The smaller adjacent angle will be 5 * 15 = 75 °, and the larger adjacent angle will be 7 * 15 = 105 °.
Answer: 75 °; 105 °.
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