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-

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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]

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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)

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

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

$2 c = 96^{\circ}$

$c = 48^{\circ}$

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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]