Question

If lines PQ and RS intersect at point T, such that ∠PRT = 40°, ∠RPT = 95° and ∠TSQ= 75°, find ∠SQT. In Fig. 6.42.​

Answer 1

Answer:

 We have,

lines PQ and RS intersect at point T, such that \angle PRT = 40°, \angle RPT = 95° and \angle TSQ = 75°

In \DeltaPRT, by using angle sum property

\anglePRT + \anglePTR + \angleTPR = 180^0

So, \anglePTR  = 180^0 -95^0-40^0

 \Rightarrow \angle PTR = 45^0

Since lines, PQ and RS intersect at point T

therefore, \anglePTR = \angleQTS (Vertically opposite angles)

               \angleQTS = 45^0

Now, in \DeltaQTS,

By using angle sum property

\angleTSQ + \angleSTQ + \angleSQT = 180^0

So, \angleSQT = 180^0-45^0-75^0

\therefore \angle SQT = 60^0

Answer 2

$\red{\boxed{\tt{Given࿐}}}$

∠PRT=40°

∠RPT=95°

∠TSQ=75°

$\red{\tt{◆To\:find◆}}$

IN ΔPRT

∠PRT+∠RTP+∠TPR=180°(∠s SUM PROPERTY)

40°+∠RTP+95°=180°

∠RTP=45°

$\purple{\boxed{\bf{NOW,}}}$ ∠RTP=∠QST=45°(VERTICALLY OPPOSITE ∠s)

NOW , IN ΔQST

∠T+∠Q+∠S=180°

45°+∠Q+75°=180°

∠Q=60°

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⠀ $&#9679\orange{\bf{diagram\: attached }}\: \green✔$

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All necessary formulas⤵️

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$\purple{\boxed{\bf{Angle\:sum\: property}}}$

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°. Proof .Thus, the sum of the interior angles of a triangle is 180°.

$\blue{\tt{Example:-}}$

$\red{\boxed{a+b+c=180°}}$

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$\orange{\boxed{\bf{Alternate\: interior\:angle}}}$

Alternate interior angles are angles formed when two parallel or non-parallel lines are intersected by a transversal.Alternate interior angles are equal if the lines intersected by the transversal are parallel.

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$\orange\star{\bf{\red{\underbrace{complementary \:angle}}}}\red\star$

The sum of 2 numbers$=90°$

example $a−b=90°$

how to find "a" if a is not mentioned

$\red{\underbrace{\bf{\orange{Given࿐}}}}$

$a= \: ?$

$b = 40$

$a+40=\:90°$

$a=90-40°$

$a=50°$

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$\pink\star{\bf{\purple{\underbrace{supplementary\: angle}}}}\red\star$

The sum of two numbers$= \:180°$

example $a+b=180°$

how to find "a" if a is not mentioned

Given

$a= \:?$

$b =\: 40$

$a+40=180°$

$a=180-40°$

$a=140°$

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$\orange\star{\bf{\green{\underbrace{Adjacent \:angle}}}}\red\star$

If there is a common ray between ${\bf&#x2220}a$ and ${\bf&#x2220}b$ so it is a adjacent angle.

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$\orange\star{\bf{\blue{\underbrace{Vertical\: opposite\: angle }}}}\red\star$

Vertical angles are pair angles formed when two lines intersect. Vertical angles are sometimes referred to as vertically opposite angles because the angles are opposite to each other.

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$\orange\star{\bf{\orange{\underbrace{lenear\: pair \:of\: angles}}}}\red\star$

Here ${\bf&#x2220}a$$+{\bf&#x2220}b$$=$180°.

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