Page 142 - Start Up Mathematics_7

9 Lines and Angles

Look closely at the photograph of any building like your house, school or neighbour’s house. You
will find that the building has been built using various concepts of lines and angles. Architects and
builders use concepts of lines and angles to construct buildings, bridges, monuments, etc.
Similarly, a carpenter uses the concept of lines and angles to make furniture.

Recall that a ray has one end point, i.e., its starting point. A line
segment has two end points and a line has no end points. When Do you know?
two lines or line segments meet, an angle is formed. The turn that The Babylonians in northern
one arm of an angle takes to reach the other arm is its magnitude. Africa were the first to use
degrees and they divided a circle
The magnitude of an angle is expressed in degrees. into 360°.

In this chapter, we will learn about pairs of related angles like
complementary angles, supplementary angles, adjacent angles, linear pair and vertically opposite
angles. Pair of intersecting lines, transversal, angles made by a transversal and condition for specific
angles to be equal will also be covered in this chapter.

Complementary Angles
Two angles are said to be complementary if the sum of their measures
is 90°. For example, ∠A = 25° and ∠B = 65° are complementary angles.

Example 1: Can two acute angles be complement of each other? 25° 65°
Solution: Yes, pairs like 50° and 40°, 30° and 60°, 45° and 45°, etc. are complements of each
other.
Example 2: Are two right angles complement of each other?
Solution: Since the sum of two right angles is 180°, therefore they are never complementary.

Example 3: Which pairs of the following angles are complementary?

52°
(a) (b)

35° 55° 48°