Question

15. PQ and RS are two chords of a circle intersecting at X. Prove that the triangles PSX and RQX are
equiangular to one another.
16. In the given figure AR and D are two mutually perpendicular​

Answer 1

Answer:

PR=PQ

⇒∠PRQ=∠PQR=2∠PQR.

So, in ΔPQR we have,

2∠PQR+∠QPR=180

o

....(angle sum property of triangles).

∴2∠PQR+30

o

=180

o

⇒∠PQR=75

o

=∠PRQ .........(i)

Again, ∠PQR=∠QSR=75

o

...(by alternate segment theorem) ...(from i)....(ii)

Also, SR∥PQ.⇒∠PQR=75

o

=∠QRS ......(iii)

∴ In ΔSRQ, we have

∠RQS+∠QSR+∠SRQ=180

o

.....(Angle Sum property of triangles.)

⇒∠RQS=180

o

−(∠QSR+∠SRQ)

⇒∠RQS=180

o

−(75

o

+75

o

)=30

o

.... (from (i) & (ii))

Answered By

toppr

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