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  1. O is the incentre of ∆ PQR and ∠QPR = 50°, then the measure of ∠QOR is :
    1. 125°
    2. 100°
    3. 130°
    4. 115°
Correct Option: D

As per the given in question , we draw a figure of triangle ABC

∠QPR = 50°
∴ ∠PQR + ∠PRQ = 180° – 50° = 130°

1
∠PQR +
1
∠PRQ = 65°
22

The point of intersection of internal bisectors of angles is in-centre.
∴ ∠OQR =
1
∠PQR ...... ( 1 )
2

∠ORQ =
1
∠PRQ ...... ( 2 )
2

In ∆ OQR,
∠OQR + ∠QOR + ∠ORQ = 180°
⇒ ∠QOR = 180° – 65° = 115° { From ( 1 ) + ( 2 ) }



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