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Standard VIII

Mathematics

Deducing Properties of Isosceles Triangles

In the given ...

Question

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

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Solution

By Exterior-angle theorem:In a triangle,the exterior angle is equal to sum of the interior opposite angles.
$∴ ∠ P T S = ∠ T P R + ∠ P R T = 95^{\circ} + 40^{\circ} = 135^{\circ}$
Again $∠ P T S = ∠ T S Q + ∠ T Q S$
$\Rightarrow 135^{\circ} = 75^{\circ} + ∠ T Q S$
$\Rightarrow ∠ T Q S = 135^{\circ} - 75^{\circ} = 60^{\circ}$
Hence $∠ S Q T = 60^{\circ}$

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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.

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

By Exterior-angle theorem:In a triangle,the exterior angle is equal to sum of the interior opposite angles.∴∠PTS=∠TPR+∠PRT=95∘+40∘=135∘Again ∠PTS=∠TSQ+∠TQS⇒135∘=75∘+∠TQS⇒∠TQS=135∘−75∘=60∘Hence ∠SQT=60∘

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