Find all the angles formed at the intersection of two parallel lines a and b secant c if one

Find all the angles formed at the intersection of two parallel lines a and b secant c if one of the angles is 40 degrees less than the other.

For ease of writing and explanation, we introduce the notation;

Parallel lines – “a” and “b”;

Secant line – “c”;

Since the straight lines “a” and “b” are parallel, the angles formed by the straight line “c” will be the same;

Therefore, consider the angles formed by the straight lines “a” and “c”;

Let’s designate the larger angle through “X”, then the smaller one will be “X – 40”;

Let’s write the equation for adjacent angles;

180 ° = X + (X – 40);

Let’s open the brackets and solve this equation;

180 ° = 2X – 40 °;

2X = 220 °;

x = 110 °;

Substitute the found value of the angle;

110 – 40 = 70 °;

Since opposite angles are equal, we get the answer;

Answer: Angles equal to 110 ° and 70 ° are formed.