Question

Two adjacent angles are said to form a linear pair of angles, if their non-common arms are two

• A. adjacent rays
• B. linear rays
• C. Multiple rays
• D. opposite rays

Hint:

Linear pair means two adjacent angles whose non-common arms are opposite rays. Their sum is \(180^\circ\).

Answer 1

The Correct Option is D

Concept:
A linear pair of angles is formed when two adjacent angles have their non-common arms in opposite directions. In simple words, the two non-common arms form a straight line. The sum of angles in a linear pair is: \[ 180^\circ \]

Step 1: Understand adjacent angles.
Two angles are adjacent if: \[ \text{they have a common vertex} \] \[ \text{they have a common arm} \] \[ \text{their interiors do not overlap} \]

Step 2: Understand linear pair.
For adjacent angles to form a linear pair, their non-common arms must make a straight line. A straight line is formed by two opposite rays. Therefore, the non-common arms must be: \[ \text{opposite rays} \]

Step 3: Use angle sum property.
If two angles form a linear pair, then: \[ \angle 1+\angle 2=180^\circ \] This happens because opposite rays form a straight angle.

Step 4: Check the options.
Option (A) adjacent rays is incorrect because adjacent rays do not necessarily form a straight line.
Option (B) linear rays is not the standard term.
Option (C) multiple rays is incorrect.
Option (D) opposite rays is correct. Hence, the correct answer is: \[ \boxed{(D)\ \text{opposite rays}} \]