NCERT Solutions Class 7 Maths Chapter 5 — Parallel & Intersecting Lines

Solution:

Step 1: Parallel lines are defined as two lines in a plane that are always the same distance apart and never intersect.

Step 2: Options A and C describe intersecting lines. Option D is irrelevant as lines are infinite in length.

Solution:

Step 1: A linear pair of angles are adjacent angles that form a straight line.

Step 2: The sum of angles in a linear pair is always 180°.

Step 3: So, ∠X + ∠Y = 180°. Given ∠X = 60°, we have 60° + ∠Y = 180°.

Step 4: Solving for ∠Y: ∠Y = 180° - 60° = 120°.

Solution:

Step 1: A transversal is a line that intersects two or more lines at different points.

Step 2: In this scenario, line 't' intersects both parallel lines 'p' and 'q' at distinct points, fitting the definition of a transversal.

Solution:

Step 1: Corresponding angles are located in the same corner at each intersection.

Step 2: If ∠1, ∠2, ∠3, ∠4 are formed at the intersection with line 'm' (say, ∠1 top-left, ∠2 top-right, ∠3 bottom-left, ∠4 bottom-right).

Step 3: And ∠5, ∠6, ∠7, ∠8 are formed at the intersection with line 'n' in the same order.

Step 4: Then ∠1 corresponds to ∠5, ∠2 corresponds to ∠6, ∠3 corresponds to ∠7, and ∠4 corresponds to ∠8.

Solution:

Step 1: When two parallel lines are intersected by a transversal, alternate interior angles are equal.

Step 2: Given that ∠P and ∠Q are alternate interior angles and lines 'r' and 's' are parallel.

Step 3: Therefore, ∠Q = ∠P.

Step 4: Since ∠P = 45°, then ∠Q = 45°.