One of the angles obtained at the intersection of two straight lines is 48 degrees. Find the rest of the angles.

When two straight lines intersect, four angles are formed, the sum of which is 360 °. Let’s designate these angles clockwise ∠1, ∠2, ∠3 and ∠4. Let ∠1 = 48 °.
∠1 and ∠3 are equal, since they are vertical angles, then:
∠1 = ∠3 = 48 °.
∠1 and ∠2 are adjacent corners (they have a common vertex and side, and their other sides are continuation of each other). The sum of adjacent angles is 180 °. Thus:
∠1 + ∠2 = 180 °.
Since ∠1 = 48 °, then:
48 ° + ∠2 = 180 °;
∠2 = 180 ° – 48 °;
∠2 = 132 °.
∠2 and ∠4 are equal, since they are vertical angles, then:
∠2 = ∠4 = 132 °.
Thus, when two straight lines intersect, angles ∠1 = 48 °, ∠2 = 132 °, ∠3 = 48 °, ∠4 = 132 ° are formed.
Examination:
∠1 + ∠2 + ∠3 + ∠4 = 360 °;
48 ° + 132 ° + 48 ° + 132 ° = 360 °;
360 ° = 360 °.
Answer: ∠1 = 48 °, ∠2 = 132 °, ∠3 = 48 °, ∠4 = 132 °.