Lines a and b are parallel, c is secant. The difference between the two angles formed by these lines is 130 degrees

Lines a and b are parallel, c is secant. The difference between the two angles formed by these lines is 130 degrees, which is the ratio of the larger of these angles to the smaller.

From the condition it is known that lines a and b are parallel, c is a secant line. It is also known that the difference between the two angles formed by these lines is 130 °. And we need to find what is the ratio of the larger of these angles to the smaller.

Let’s start by saying that the two angles mentioned in the statement are adjacent. Let us recall the theorem on the sum of adjacent angles.

So, the sum of adjacent angles is 180 °.

Let’s denote by x – a smaller angle, then a larger angle:

x + x + 130 = 180;

2x = 180 – 130;

2x = 50;

x = 25 ° smaller angle.

Then the larger one:

25 ° + 130 ° = 155 °.

Angle ratio:

155/25 = 31/5 = 6.2.