The sum of the two angles, which are obtained when two lines intersect, is 60 (degrees). Find the degree measure of these angles.

When two straight lines intersect, four angles ∠1, ∠2, ∠3 and ∠4 are formed. The pairs of angles ∠1 and 2 and ∠3 and ∠4 are adjacent, and the sum of the adjacent angles is 180 °. Since in the condition it is given that the sum of two angles is 60 °, then this pair of angles is not adjacent.
1. Let:
∠1 + ∠3 = 60 °
∠1 and ∠3 are vertical, their degree measures are equal.
Let ∠1 = ∠3 = x, then:
x + x = 60 °;
2 * x = 60 °;
x = 60 ° / 2;
x = 30 °.
Thus, ∠1 = ∠3 = x = 30 °.
2.∠1 + ∠2 = 180 °;
30 ° + ∠2 = 180 °;
∠2 = 180 ° – 30 °;
∠2 = 150 °.
Thus, ∠2 = ∠4 = 150 °.
Answer: ∠1 = ∠3 = 30 °; ∠2 = ∠4 = 150 °.