Question:
In the below figure, ∠AOC and ∠BOC form a linear pair. If a - 2b = 30°, find a and b?
Solution:
Given that,
∠AOC and ∠BOC form a linear pair
If a - b = 30
∠AOC = a°, ∠BOC = b°
Therefore, a + b = 180 ... (1)
Given a - 2b = 30 ... (2)
By subtracting (1) and (2)
a + b - a + 2b = 180 - 30
3b = 150
b = 150/3
b = 50
Since a - 2b = 30
a - 2(50) = 30
a = 30 + 100
a = 130
Hence, the values of a and b are 130° and 50° respectively.