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In given fig., if (x)/(3)=(y)/(4)=(z)/(5...

In given fig., if `(x)/(3)=(y)/(4)=(z)/(5)` , then calculate the values of x,y and z.

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In the figure, `(x)/(3)=(y)/(4)=(z)/(5)=k` (say)
`rArrx=3k`
`y=4k`
and `z=5k`
In cyclic qudarilateral ABCD, the side BC is produced to Q.
`thereforeangle A= angle DCQ=x` (`because` exterior angle of a cyclic quadrilateral is equal to its interior opposite angle)
Also, in `DeltaCDQ`, the side QD is produced to A
`rArrangle ADP=x+z` (`because` exterior angle of a triangle is equal to the sum of its two int., opposite angles)
Now, in `DeltaADP`,
`angleA+ angle ADP+angle APD=180^@` (`because` sum of angles of a triangle is `180^@`)
`thereforex+(x=z)+y=180^@`
`rArr 2x+y+z=180^@`
`rArr2(3k)+4k+5k=180^@`
`rArr6k+4k+5k=180^@`
`rArr15k=180^@rArrk=180^@div15=12^@`
`thereforex=3k=3xx12=36^@`
`y=4k=4xx12=48^@`
and `z=5k=5xx12=60^@`
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