Consider the following parallelograms. Find the values of the unknowns `x, y, z`.

Explanation

(i)Since D is opposite to B.
So,`y=100^@`
(Since oppositeanglesofparallelogram areequal)`angleB+angleC= 180^@`
(The adjacent angles in a parallelogram are supplementary
`x+100^@= 180^@`Therefore `180^@ -100^@=80^@`

`x=z=80^@`[Since opposite angles of a parallelogram are equal]and adjacent angles are supplementary.]
Using this property, we cancalculate the measure of the unknown angles.]
Solution:]

`x^@+50^@=180^@`
`x=180^@-50^@`

`x=130^@`
`x=y=130^@`
(The adjacent angles in aparallelogramaresupplementary )]
(Since opposite angles of a parallelogram are equal)`x= z =130^@`
(Corresponding angle

(iii)In a parallelogram, opposite angles are equal
and adjacent angles are supplementary.Using this property,
wecancalculate the measure of the unknown angles.
Solution

`z=80^@` (Corresponding angles)
`y=80^@` (since oppositeanglesofaparallelogramareequal
`x+y=180^@`(Adjacentanglesaresupplementary
`x+80^@=180^@`
`x=180^@-80^@`

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