Question

In the figure, ∠POR and ∠QOR form a linear pair. If a – b = 80°, then the values of ‘a’ and ‘b’ are:-

a) a = 50°, b = 130°
b) a = 130°, b = 50°
c) a = 260°, b = 60°
d) a = 60°, b = 260°

Answer 1

Hint: We know that the sum of the measures of the angles of a linear pair is always 180°. In other words, a linear pair is supplementary.

Complete step-by-step answer:
Two angles are said to be linear if they are adjacent and are formed by two intersecting lines. The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees.
As ∠POR and ∠QOR are forming a linear pair and the difference between the angles ‘a’ and ‘b’ is 80°, therefore, b = (a – 80)
a + b = 180° (linear pair)
a + (a – 80) = 180°
a + a – 80 = 180°
2a = 260°
a = 130°
Therefore, b = (a – 80) =130 – 80 = 50°
Hence, the answer is (b) a = 130°, b = 50°

Note: Many students get confused between adjacent angles and linear pairs.
Adjacent angles are two angles that have a common vertex and a common side but do not overlap.

This is an example of adjacent angles. They have a common side and a common arm, but they are not supplementary.
Two angles are said to be linear if they are adjacent and are formed by two intersecting lines. The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees.

So, the main difference between adjacent angles and a linear pair is that a linear pair must be supplementary while adjacent angles are not necessarily supplementary.