Beam BD divides the swept angle ABC into two angles with a difference of 46 degrees. Find the angles that form.

Let us denote by the variable n the number of degrees, which corresponds to the value of the larger of the two formed angles.

Accordingly, according to the conditions of this task, the number of degrees, which corresponds to the value of the smaller of the two formed angles, we can represent in the form (n – 46).

Since we know that these angles form an extended angle ABC, which means their sum is 180 °, we write the equation and find these angles:

n + n – 46 = 180;

2n = 226;

n = 113;

180 – 113 = 67.

Answer: 67 ° and 113 °.