A flattened angle is divided by a ray from its vertex into two angles such that 40% of one angle is equal to 2/13

A flattened angle is divided by a ray from its vertex into two angles such that 40% of one angle is equal to 2/13 of the other. Find how many degrees the greater of these angles is greater than the right angle.

Let’s take the first angle as x, then, given that the angles adjacent to the second will be equal to 180 ° – x.

From the condition of the problem we write down the equation and solve:

x * 4/10 = (180 – x) * 2/13;

x * 4/10 = 2 * 180/13 – x * 2/13;

x * 4/10 + x * 2/13 = 360/13;

(52 * x + 20 * x) / 130 = 360/13;

(72 * x) / 130 = 360/13;

72 * x = 130 * 360/13;

x = 3600/72;

x = 50.

The first angle is 50 °, so the thief will be equal to: 180 ° – 50 ° = 130 °. This is a larger angle.

It differs from a right angle by: 130 ° – 90 ° = 40 °.

Answer: 40 °.