Question

$\huge\mathfrak\color{red}{Question}$

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

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Answer 1

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Answer 2

$\huge\mathfrak{\color{orange}{\underline {\underline{Answer♡}}}}$

${\tt {\red {\underline{\underline {\bold {Given}}}}}}$

• ∠PRT = 40°

• ∠RPT = 95°

• ∠TSQ = 75°

${\tt {\red {\underline{\underline {\bold {To\: Find }}}}}}$

• ∠SQT = ?

${\tt {\red {\underline{\underline {\bold {Solution}}}}}}$

➜ ∠PRT + ∠RPT + ∠RTP = 180° [ Angle Sum Property]

➜40° + 95° + ∠RTP = 180°

➜∠RTP + 135° = 180°

➜∠RTP = 180° - 135°

➜∠RTP = 45°

So, ∠RTP = ∠STQ = 45° [ Vertically Opposite Angle ]

➜∠STQ + ∠TSQ + ∠SQT = 180°[Angle Sum Property ]

➜45° + 75° + ∠SQT = 180°

➜∠SQT + 120° = 180°

➜∠ SQT = 180° - 120°

➜∠SQT = 60°

$\large\purple{\boxed{✏More\: Information}}$

• When two lines intersect each other, then the opposite angles, formed due to intersection are called vertical angles or vertically opposite angles.

• Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.