In the figure- two straight lines PQ and RS intersect each other at O- If - POT -75- find the values of a - b and c- -4 MARKS-2 c

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Vertically Opposite Angles

In the figure...

Question

In the figure, two straight lines PQ and RS intersect each other at O. If $∠ P O T = 75^{\circ}$ , find the values of a, b and c. [4 MARKS]

Open in App

Solution

Concept: 1 Mark
Application: 1.5 Marks
Answer: 0.5 Mark each

ROS is a straight line.

$∠ R O P + ∠ P O T + ∠ T O S = 180^{\circ}$

$4 b + 75^{\circ} + b = 180^{\circ}$

$5 b + 75^{\circ} = 180^{\circ}$

$5 b = 180^{\circ} - 75^{\circ}$

$b = 21^{\circ}$

Since,PQ and RS intersect at O.

$∠ Q O S = ∠ P O R$ [Vertically opposite angles]

$a = 4 b$

$a = 4 \times 21^{\circ} = 84^{\circ}$

$∠ R O Q = ∠ P O S$ (vertically opposite angles)

$2 c = 75^{\circ} + b$

$2 c = 75^{\circ} + 21^{\circ}$

$2 c = 96^{\circ}$

$c = 48^{\circ}$

Suggest Corrections

385

Similar questions

Q. In the given figure,

P Q

and

R S

intersect each other at

O

. If

∠ R O T = 75^{o}

, find the value of

c

Q. In the given figure,

P Q

and

R S

are two lines intersecting each other at point

^{'} O^{'}

. If

∠ P O S = 90^{\circ}

. Find the value of

x, y

and

z

In the figure, lines PQ and RS intersect each other at point O; ray OA and ray OB bisect $∠ P O R$ and $∠ P O S$ respectively. If $∠ P O A : ∠ P O B = 2 : 7$ , then find $∠ S O Q$ and $∠ B O Q$ . [4 MARKS]

In the figure below, lines RS and PQ intersect each other at point O. If $∠ P O R$ : $∠ R O Q$ = 11:13, find $∠ S O Q$ .

In the figure, lines PQ and RS intersect each other at point O. If $∠ P O R : ∠ R O Q = 5 : 7$ . Find all the angles.

Join BYJU'S Learning Program

In the figure, two straight lines PQ and RS intersect each other at O. If ∠POT=75∘, find the values of a, b and c. [4 MARKS]

In the figure, two straight lines PQ and RS intersect each other at O. If $∠ P O T = 75^{\circ}$ , find the values of a, b and c. [4 MARKS]