Beam OF, drawn from the vertex of the right angle COB, divides it into the angles COF

Beam OF, drawn from the vertex of the right angle COB, divides it into the angles COF and BOF. The ratio of the degree measures is 5: 4. Find the degree measures of the angles COF and BOF?

Let us denote by the variable x the number of degrees of the right angle, which falls on one part.

Therefore, according to the condition of the problem, the degree value of the COF angle can be expressed through 5x, and the degree value of the BOF angle can be expressed through 4x.

Knowing that the angles COF and BOF form a right angle COB, the degree value of which, by definition, is equal to 90 °, we draw up an equation and determine these angles:

5x + 4x = 90;

9x = 90;

x = 10;

5 * 10 = 50;

90 – 50 = 40.

Answer: The COF angle is 50 °, the BOF angle is 40 °.