In the given figure- O is the centre of the circle and - QPR - x- - ORQ - y- Which statement is true about x- and y-

The correct option is B x^∘ + y^∘ = 90^∘ In OQR OR=OQ= radius ⇒∠ OQR=∠ ORQ=y^o Thus by angle sum property, we have ∠ OQR+∠ ORQ+∠ QOR=180^ ...

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Byju's Answer

Standard IX

Mathematics

Angle Subtended by an Arc of a Circle on the Circle and at the Center

In the given ...

Question

In the given figure, $O$ is the centre of the circle and $∠ Q P R = x^{\circ}; ∠ O R Q = y^{\circ}$ . Which statement is true about $x^{\circ}$ and $y^{\circ}$ ?

x^{\circ} + y^{\circ} = 120^{\circ}

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x^{\circ} + y^{\circ} = 180^{\circ}

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x^{\circ} + y^{\circ} = 90^{\circ}

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x^{\circ} + y^{\circ} = 150^{\circ}

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Solution

The correct option is B $x^{\circ} + y^{\circ} = 90^{\circ}$
In $△ O Q R O R = O Q =$ radius
$\Rightarrow ∠ O Q R = ∠ O R Q = y^{o}$
Thus by angle sum property, we have
$∠ O Q R + ∠ O R Q + ∠ Q O R = 180^{o} 2 ∠ O R Q + ∠ Q O R = 180^{o} ∠ Q O R = 180 - 2 ∠ O R Q = 180 - 2 x^{o}$
Also, $∠ Q O R = 2 ∠ Q P R$ (half angle property)
$180 - 2 x = 2 y 180 = 2 x + 2 y x^{o} + y^{o} = 90^{o}$

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In the given figure, O is the centre of the circle and ∠QPR=x∘;∠ORQ=y∘. Which statement is true about x∘ and y∘?

The correct option is B x∘+y∘=90∘In △OQROR=OQ= radius⇒∠OQR=∠ORQ=yoThus by angle sum property, we have∠OQR+∠ORQ+∠QOR=180o2∠ORQ+∠QOR=180o∠QOR=180−2∠ORQ=180−2xoAlso, ∠QOR=2∠QPR (half angle property)180−2x=2y180=2x+2yxo+yo=90o

In the given figure, $O$ is the centre of the circle and $∠ Q P R = x^{\circ}; ∠ O R Q = y^{\circ}$ . Which statement is true about $x^{\circ}$ and $y^{\circ}$ ?