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Question
In following figure , Δ PQR is an isosceles teiangle with PQ = PR and m ∠ PQR = 35° .Find m ∠ QSR and ∠ QTR
Solution
In Δ PQR.,
PQ = PR
∴ ∠ PQR = ∠ PRQ = 35°
Also , ∠ PQR + ∠ PRQ + ∠QPR = 180°
35 + 35 + ∠QPR = 180
∠QPR = 110°
In cyclic quadrilateral PQSR ,
∠QPR + ∠QSR = 180
110 + ∠QSR = 180
∠QSR = 70
Also , ∠QSR = ∠QTR = 70° (Angles in the same segment)
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Given: ABCD is cyclic,
`square` is the exterior angle of ABCD
To prove: ∠DCE ≅ ∠BAD
Proof: `square` + ∠BCD = `square` .....[Angles in linear pair] (I)
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