In fig- if line PQ and RS intersect at point T- such that - P RT -40- - RPT -95- and - T SQ -75- find - SQT- -4 MARKS-

Concept: 2 Marks Application: 2 Marks In Δ PRT ⇒∠ PTR + ∠ PRT + ∠ RPT = 180^∘ (since the sum of the angles of a triangle is 180^∘) ⇒∠ PTR + 40^∘ + 95^∘ = 18 ...

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Byju's Answer

Standard IX

Mathematics

Adjacent Angles

In fig, if li...

Question

In fig, if line PQ and RS intersect at point T, such that $∠ P R T = 40^{\circ}$ , $∠ R P T = 95^{\circ}$ and $∠ T S Q = 75^{\circ}$ , find $∠ S Q T$ . [4 MARKS]

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Solution

Concept: 2 Marks
Application: 2 Marks

In $Δ P R T$

$\Rightarrow ∠ P T R + ∠ P R T + ∠ R P T = 180^{\circ}$ (since the sum of the angles of a triangle is $180^{\circ}$ )

$\Rightarrow ∠ P T R + 40^{\circ} + 95^{\circ} = 180^{\circ}$

$\Rightarrow ∠ P T R + 135^{\circ} = 180^{\circ}$

$\Rightarrow ∠ P T R = 180^{\circ} - 135^{\circ}$

$\Rightarrow ∠ P T R = 45^{\circ}$

$\Rightarrow ∠ Q T S = ∠ P T R = 45^{\circ}$ (Vertically Opposite angles)

In $Δ T S Q$

$\Rightarrow ∠ Q T S + ∠ T S Q + ∠ S Q T = 180^{\circ}$ (since the sum of the angles of a triangle is $180^{\circ}$ )

$\Rightarrow ∠ S Q T + 45^{\circ} + 75^{\circ} = 180^{\circ}$

$\Rightarrow ∠ S Q T + 120^{\circ} = 180^{\circ}$

$\Rightarrow ∠ S Q T = 180^{\circ} - 120^{\circ}$

$\Rightarrow ∠ S Q T = 60^{\circ}$

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Q. In the figure, if lines

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In the given figure, if lines PQ and RS intersect at point T, such that ∠PRT = 40º, ∠RPT = 95º and ∠TSQ = 75º, find ∠SQT.

In the given figure, if lines PQ and RS intersect at point T, such that $∠ P R T = 40^{\circ}, ∠ R P T = 95^{\circ} a n d ∠ T S Q = 75^{\circ}$ , find $∠ S Q T .$