Lines AB and CD are parallel and P is any point as shown in the figure. Find the value of x0
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answer ABP+ angle CDP --angle DPB
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- Draw a line GH passing through the point P which is parallel to both AB and CD. Here, BD is the transversal.
We know that,
- Angles on the same side of transversal are supplementary i.e., their sum is equal to 180°.
Therefore,
⇒ ∠ABP + ∠BPG = 180°
⇒ 116° + ∠BPG = 180°
⇒ ∠BPG = 180° - 116°
⇒ ∠BPG = 64°
Similarly,
⇒ ∠CDP + ∠DPG = 180°
⇒ 124° + ∠DPG = 180°
⇒ ∠DPG = 180° - 124°
⇒ ∠DPG = 56°
Now,
⇒ x° = ∠BPG + ∠DPG
⇒ x° = 64° + 56°
⇒ x° = 120°
•°• The required value of x is 120°.
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