Find all the angles formed at the intersection of two parallel secant lines if one of them is 24 degrees

Find all the angles formed at the intersection of two parallel secant lines if one of them is 24 degrees less than the other.

When two straight lines intersect, two pairs of adjacent corners are formed. In turn, they make up two pairs of equal vertical angles.

Let one of the adjacent angles be x degrees, then the second of the adjacent angles is x + 24 degrees. We know that the sum of the degree measures of adjacent angles is 180 degrees. Let’s make the equation:

x + x + 24 = 180;

x + x = 180 – 24;

x + x = 156;

x * (1 + 1) = 156;

x * 2 = 156 (in order to find an unknown factor, you need to divide the product by a known factor);

x = 156: 2;

x = 78 degrees – one of the adjacent angles;

78 + 24 = 102 degrees – the second of the adjacent angles.

Answer: 78 degrees; 78 degrees; 102 degrees; 102 degrees.