In the given figure, $P Q = P R$ , find $∠ Q T R$ .

35^{\circ}

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70^{\circ}

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110^{\circ}

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90^{\circ}

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Solution

The correct option is B $70^{\circ}$
$P Q = P R \Rightarrow ∠ P Q R = ∠ P R Q (A n g l e s a l o n g t h e s a m e s i d e a r e e q u a l) ∠ P R Q = 35 (G i v e n) \Rightarrow ∠ P Q R = 35 I n △ P Q R ∠ P Q R + ∠ P R Q + ∠ Q P R = 180 (A n g l e s u m p r o p e r t y) \Rightarrow 35 + 35 + ∠ Q P R = 180 \Rightarrow 70 + ∠ Q P R = 180 \Rightarrow ∠ Q P R = 180 - 70 = 110... (1) N o w P Q T R i s a c y c l i c q u a d i l a t e r a l ∠ Q P R + ∠ Q T R = 180 \Rightarrow ∠ Q T R = 180 - ∠ Q P R \Rightarrow ∠ Q T R = 180 - 110 [F r o m (1)] \Rightarrow ∠ Q T R = 70 O p t i o n (B) i s t h e c o r r e c t a n s w e r$

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