In Fig. 8.39, POS is a line, find x.
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Answer:
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Given : POS is a line.From figure we have , ∠POQ = 60°, ∠ROQ = 4x, ∠ROS = 40°
Concept :
Linear pair of angles:
If non-common arms of two adjacent angles form a line, then these angles are called linear pair of angles.
Axiom- 1
If a ray stands on a line, then the sum of two adjacent angles so formed is 180°i.e, the sum of the linear pair is 180°.
Axiom-2
If the sum of two adjacent angles is 180° then the two non common arms of the angles form a line.
The two axioms given above together are called the linear pair axioms.
Solution :
∠POQ + ∠QOS = 180° [Linear pair]
∠POQ + ∠ROQ + ∠ROS = 180°
60° + 4x + 40° = 180°
100° + 4x ° = 180°
4x ° = 180° - 100°
4x = 80°
x = 80°/4
x = 20°
Hence the value of x is 20°.
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