The difference between the two angles resulting from the intersection of two straight lines is 46 °. Find these angles.

Two straight lines AB and CD intersect at point O. When two straight lines intersect, 4 angles are formed: angle AOC, angle COB, angle BOD, angle DOA (these angles add up to 360 degrees). Angle AOC = angle BOD = x and angle COB = angle DOA = y – since they are vertical. The AOC angle and the COB angle are adjacent (their sum is 180 degrees). Then we get a system of linear equations with two unknowns:
x + y = 180;
x – y = 46.
In the first equation, we express x through y:
x = 180 – y.
Substitute the resulting expression into the second equation of the SLN and find the value of y:
180 – y – y = 46;
-2y = 46 – 180;
-2y = -134;
y = 134/2;
y = 67.
COB angle = DOA angle = y = 67 degrees.
We substitute the obtained value y into the first equation of the SLN:
x + 67 = 180;
x = 180 – 67;
x = 113.
Angle AOC = angle BOD = x = 113 degrees.
Answer: COB angle = DOA angle = 67 degrees, AOC angle = BOD angle = 113 degrees.