Question

Q7. In the given figure AB || CD. Find the value of <PQR.
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Answer 1

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Answer 2

${\huge{\underline{\underline{\sf{\blue{Given :-}}}}}}$

⠀⠀

⠀⠀ • AB || CD

⠀⠀ • ∠BPQ= 40°

⠀⠀ • ∠QRD = 55°

⠀⠀

${\huge{\underline{\underline{\sf{\blue{To\: Calculate :-}}}}}}$

⠀⠀

⠀⠀ • ∠PQR = ?

⠀⠀

${\huge{\underline{\underline{\sf{\blue{ Construction :-}}}}}}$

⠀⠀

⠀⠀ • Draw a line ST parallel to AB and CD

⠀⠀

${\huge{\underline{\underline{\sf{\blue{Explanation :-}}}}}}$

⠀⠀ • ∠BPQ= 40°

⠀⠀ • ∠QRD = 55°

∠BPQ= ∠PQS = 40°( Alternate int. Angles)

⠀⠀⠀⠀∠PQS= 40°

∠DRQ= ∠QRC= 55°( Alternate int. angles)⠀

⠀⠀⠀⠀∠QRS = 55°

So Angle ∠PQR = 40+55 = 95°

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${\huge{\underline{\underline{\sf{\blue{Hence :-}}}}}}$

⠀⠀

⠀⠀⠀⠀⠀⠀ • ∠PQR= 95°

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