Question

If the sum of the interior angles which are lying on the same side of the transversal is supplementary, then the lines are parallel. If true, enter 1, else 0.

Answer 1

HINT:- Before solving this question, we must know about Parallel lines and Transversal.
PARALLEL LINES: Parallel lines are the lines in a plane which never meet each other even on extending, i.e., two straight lines in a plane that do not intersect at any point are said to be parallel.
TRANSVERSAL: A transversal is a line that passes through two lines in the same plane at two distinct points.

Complete step-by-step answer:
When a transversal cuts two parallel lines, then a lot of angles are formed. All of them are mentioned in the note below. One of these angles is Co – Interior Angles.
The interior Angles that lie on the same side of the transversal are known as co – interior angles.
The sum of these angles is 180°. In other words, these angles are supplementary.
Also, the sum of the co – interior angles will only be 180° if the lines are parallel.
So, similarly, if the sum of the co – interior angles is 180°, then the two lines must be parallel.
Hence, the answer of this question is true, i.e. 1.

NOTE:- Let us now know about the different angles formed when a transversal cuts two parallel lines.

LINEAR PAIRS
Their sum is equal to 180°.
i. 1 and 2
ii. 4 and 3
iii. 5 and 6
iv. 8 and 7
v. 1 and 4
vi. 2 and 3
vii. 5 and 8
viii. 6 and 7

VERTICALLY OPPOSITE ANGLES
i) 1 and 3
ii) 2 and 4
iii) 5 and 7
iv) 6 and 8

CORRESPONDING ANGLES
i) 1 and 5
ii) 2 and 6
iii) 4 and 8
iv) 3 and 7

ALTERNATE INTERIOR ANGLES
i) 4 and 6
ii) 5 and 3

ALTERNATE EXTERIOR ANGLES
i) 1 and 7
ii) 8 and 2

CO – INTERIOR ANGLES
i) 4 and 5
ii) 3 and 6

CO – EXTERIOR ANGLES
i) 1 and 8
ii) 2 and 7

It is very important to solve this question very carefully as if there is any mistake; the answer can come out to be wrong.