1.

PQRS is a cyclic Quadrilateral PQ = PS and QR = QS. If 4 QRS = 70°,find the angles marked a, x and y.​

Answer»

Step-by-step explanation:

⇒ In FIGURE, PQRS is a cyclic quadrilateral.

⇒ The sides PS and QR are produced to MEET at B.

⇒ ∠QPB=∠QPR+∠RPS=40

o

+35

o

=75

o

---- ( 1 )

⇒ In △PBQ

⇒ ∠PBQ+∠BQP+∠QPB=180

o

[ Sum of ANGLES of triangle is 180

o

]

⇒ 30

o

+∠BQP+∠75

o

=180

o

⇒ ∠BQP=180

o

−105

o

∴ ∠BQP=75

o

--- ( 2 )

∴ ∠QPB=∠BQP [ From ( 1 ) and ( 2 ) ]

∴ △PBQ is isosceles triangle.

∴ PB=QB [ Sides of isosceles triangle ]

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