When two straight lines intersect, 4 corners are formed. It is known that the degree measure of one

When two straight lines intersect, 4 corners are formed. It is known that the degree measure of one of the angles is 24 degrees greater than the other. Find the degree measure of all angles.

Given:
AC intersects with BE at point O,
angle AOB and angle BOC are adjacent,
angle AOB = angle BOC + 24 degrees.
Find the degree measures of the AOB angle and the BOC angle, the AOE angle, the COE angle -?
Solution:
1) Consider the adjacent angles AOB and BOС. Let the angle BОС = x degrees, then the angle AOB = 56 + x degrees. We know that the sum of the degree measures of adjacent angles is 180 degrees. Let’s make the equation:
x + 56 + x = 180;
x + x = 180 – 56;
x + x = 124;
x * (1 + 1) = 124;
x * 2 = 124;
x = 124: 2;
x = 62 degrees – the degree measure of the BОС angle;
56 + 62 = 118 degrees – the degree measure of the angle AOB;
Angle BOC = angle AOE = 62 degrees, since they are vertical;
angle AOB = angle COE = 118 degrees.
Answer: 118 degrees; 62 degrees; 62 degrees; 118 degrees.