In the given figure- chords PQ-RS- - POQ-75- and - POS-150-Find the value of - QOR-

We know that equal chords of a circle subtend equal angles nbsp;at the centre. ⇒∠ POQ=∠ ROS=75^∘ Since, the central angle of a circle is 360^∘ So, ∠ POQ+∠ ...

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Standard X

Mathematics

Theorem of Equal Chords Subtending Equal Angles at the Center

In the given ...

Question

In the given figure, chords $P Q = R S, ∠ P O Q = 75^{\circ}$ and $∠ P O S = 150^{\circ}$ .

Find the value of $∠ Q O R$ .

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Solution

We know that equal chords of a circle subtend equal angles at the centre.

$\Rightarrow ∠ P O Q = ∠ R O S = 75^{\circ}$

Since, the central angle of a circle is $360^{\circ}$

So, $∠ P O Q + ∠ Q O R + ∠ R O S + ∠ P O S = 360^{\circ}$

$\Rightarrow 75^{\circ} + ∠ Q O R + 75^{\circ} + 150^{\circ} = 360^{\circ}$

$\Rightarrow 300^{\circ} + ∠ Q O R = 360^{\circ}$

$\Rightarrow ∠ Q O R = 360^{\circ} - 300^{\circ} = 60^{\circ}$

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Similar questions

The given figure shown a circle with centre O. Also, PQ = QR = RS and $∠$ PTS = $75^{o}$ . Calculate :

(i) $∠$ POS,

(ii) $∠$ QOR,

(iii) $∠$ PQR.

Q. The given figure shows a circle with centre

O

. Also,

P Q = Q R = R S

and

∠ P T S = 75^{o}

. Calculate:
i)

∠ P O S

,
ii)

∠ Q O R

,
iii)

∠ P Q R

Q. In the given figure, OP, OQ, OR and OS are four rays. Prove that:
∠POQ + ∠QOR + ∠SOR + ∠POS = 360°

In the figure below, OP, OQ, OR and OS are four rays. Then, find $\frac{(∠ P O Q + ∠ Q O R + ∠ S O R + ∠ P O S)}{3}$ .

Q. In figure

O P, O Q, O R

and

O S

are four rays. Prove that

∠ P O Q + ∠ Q O R + ∠ S O R + ∠ P O S = 360^{o}

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In the given figure, chords PQ=RS, ∠POQ=75∘ and ∠POS=150∘. Find the value of ∠QOR.

We know that equal chords of a circle subtend equal angles at the centre. ⇒∠POQ=∠ROS=75∘ Since, the central angle of a circle is 360∘ So, ∠POQ+∠QOR+∠ROS+∠POS=360∘ ⇒75∘ +∠QOR+75∘ +150∘ =360∘ ⇒300∘ +∠QOR=360∘ ⇒∠QOR=360∘ −300∘ =60∘

In the given figure, chords $P Q = R S, ∠ P O Q = 75^{\circ}$ and $∠ P O S = 150^{\circ}$ .

Find the value of $∠ Q O R$ .