CBSE Class 7 Mathematics Lines and Angles Notes Set 07

Basic Terms

A point has no length or breadth. A line segment has two end points and a definite length, a ray has one end point and extends endlessly in one direction, and a line extends endlessly both ways. An angle is formed when two rays start from the same point (the vertex).
Angles are named by size: acute (less than 90°), right (90°), obtuse (between 90° and 180°), straight (180°), reflex (more than 180°) and complete (360°).

Pairs of Angles

Two angles are complementary if their sum is 90° and supplementary if their sum is 180°. Adjacent angles share a vertex and an arm, with their other arms on opposite sides of the common arm. A linear pair is a pair of adjacent angles whose non-common arms are opposite rays, so it adds to 180°.
When two lines intersect, the angles facing each other (vertically opposite angles) are equal. Angles on one side of a line add up to 180°, and angles around a point add up to 360°.

Transversal and Parallel Lines

A transversal cuts two or more lines at distinct points. It forms corresponding angles, alternate interior angles, alternate exterior angles and co-interior (same-side interior) angles.
If the two lines are parallel, corresponding angles and alternate angles are equal and co-interior angles are supplementary. The converse is also true, and is used to prove that two lines are parallel.

Worked Example

Parallel lines l and m are cut by a transversal. A pair of co-interior angles are 2x and 3x - 30. Then 2x + 3x - 30 = 180, so x = 42. The angles are 84° and 96°.