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In Fig 3.31 HELP is a parallelogram. (Le...

In Fig 3.31 HELP is a parallelogram. (Lengths are in cms). Given that `OE=4` and `HL` is 5 more than PE`? Find `OH.`

Text Solution

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ABCD isaconvexquadrilateral
made of two triangles ∆ABC and ∆ADC. We know thatthe sum of the angles of a
triangle is 180 degree. So:
`angle 6+angle 5+angle4=180^@`(sum of anglesof`triangleABC=180^@`
`angle1+angle2+angle3=180^@`(sum oftheangles of `triangleADC=180^@`
addingweget
`angle6+angle5+angle4+angle1+angle2+angle3`
`=180^@+180^@`
`=360`
Using the angle sum propertyoftriangle, again ABCD is a
concave quadrilateral,madeoftwo`triangleABD`and`triangleBCD` .
Therefore, the sum of all theinterioranglesofthis
quadrilateral will also be
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