In the given figure, $∠ P O R + ∠ Q O S = 110^{0} .$ Find $∠ R O S .$

110 degrees

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80 degrees

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90 degrees

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70 degrees

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Solution

The correct option is D 70 degrees
$∴ ∠ P O R + ∠ R O S + ∠ S O Q = 180^{0}$
$\Rightarrow ∠ P O R + ∠ S O Q + ∠ R O S = 180^{0}$
$\Rightarrow 110^{0} + ∠ R O S = 180^{0}$
$\Rightarrow ∠ R O S = 70^{0}$

So, option d is correct.

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Similar questions

Question 22

In the given figure, $∠ R O S$ is a right angle and $∠ P O R$ and $∠ Q O S$ are in the ratio 1:5. Then, $∠ Q O S$ measures

(a) $150^{\circ}$
(b) $75^{\circ}$
(c) $45^{\circ}$
(d) $60^{\circ}$

Q. In Fig., ∠POQ ≅ ∠ROS, can we say that ∠POR ≅ ∠QOS

Q. In the given figure, POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR. Prove that ∠ROS =

\frac{1}{2}

(∠QOS − POS).

Q. In the given figure

\leftarrow \to P Q

is a line. Ray

- - \to O R

is perpendicular to line

\leftarrow \to P Q . - - \to O S

is another ray lying between rays

- - \to O P

and

- - \to O R

.
Prove that

∠ R O S = \frac{1}{2} (∠ Q O S - ∠ P O S)

Q. In figure, POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR. If

∠ R O S = \frac{1}{k} (∠ Q O S - ∠ P O S)

, find

k

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In the given figure, ∠POR+∠QOS=1100. Find ∠ROS.

The correct option is D 70 degrees∴∠POR+∠ROS+∠SOQ=1800 ⇒∠POR+∠SOQ+∠ROS=1800 ⇒1100+∠ROS=1800 ⇒∠ROS=700 So, option d is correct.

In the given figure, $∠ P O R + ∠ Q O S = 110^{0} .$ Find $∠ R O S .$

The correct option is D 70 degrees
$∴ ∠ P O R + ∠ R O S + ∠ S O Q = 180^{0}$
$\Rightarrow ∠ P O R + ∠ S O Q + ∠ R O S = 180^{0}$
$\Rightarrow 110^{0} + ∠ R O S = 180^{0}$
$\Rightarrow ∠ R O S = 70^{0}$

So, option d is correct.