Let OA, OB, OC and OD are rays in the anticlockwise direction such that ∠ AOB = ∠COD = 100°, ∠BOC = 82° and ∠AOD = 78°. Is it true to say that AOC and BOD are lines
Solution:
Given, OA, OB, OC and OD are rays in the anticlockwise direction.
∠ AOB = ∠COD = 100°
∠BOC = 82°
∠AOD = 78°
We have to determine if AOC and BOD are lines or not.
If AOC is a line the linear pair of angles must be equal to 180°
So, ∠AOB + ∠COB = ∠AOC
∠AOC = 110° + 82°
∠AOC = 192°
∠AOC is not equal to 180°
Therefore, AOC is not a line.
Similarly, ∠BOC + ∠COD = ∠BOD
∠BOD = 82° + 100°
∠BOD = 182°
∠BOD is not equal to 180°
Therefore, BOD is not a line.
✦ Try This: Can two adjacent angles be complementary?
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 6
NCERT Exemplar Class 9 Maths Exercise 6.2 Sample Problem 1
Let OA, OB, OC and OD are rays in the anticlockwise direction such that ∠ AOB = ∠COD = 100°, ∠BOC = 82° and ∠AOD = 78°. Is it true to say that AOC and BOD are lines
Summary:
Let OA, OB, OC and OD are rays in the anticlockwise direction such that ∠ AOB = ∠COD = 100°, ∠BOC = 82° and ∠AOD = 78°. It is clear that AOC and BOD are not lines
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