Question

Polygon ABCD is a parallelogram, and
`m`∠
`ABC`. The length of is 10 units, and the length of is 5 units.

The perimeter of the parallelogram is [Blank]
units, and
`m`∠
`BCD` is [Blank]°

Answer 1

Polygon ABCD is a parallelogram
m<ABC = m<ADC = 127

360 - 2(127) = 360 - 254 = 106

m<BCD = m<BAD = 106/2 = 53
P = 2(10 + 5) = 2(15) = 30

answer
The perimeter of the parallelogram is 30 units, and m<BCD is 53°

Answer 2

Answer:The perimeter is
`30` unit and
`m\angle BCD=53^(\circ)`

Explanation: Since, here ABCD is a parallelogram in which,
`m\angle ABC=127^(\circ)` and sides are 10 unit and 5 unit.

And, we know, a parallelogram has two same pairs of opposite angles and has two same pairs of opposite sides.

Therefore, According to the above property of parallelogram,

`m\angle ABC=m\angle CDA` and
`m\angle BAC=m\angle BCD`

Moreover, we know that the sum of all angles of a parallelogram is
`360^(\circ)`

Thus,

`m\angle ABC+m\angle CDA+m\angle BAC+m\angle BCD=360^(\circ)`

⇒
`2* m\angle ABC+2* m\angle BCD=360^(\circ)`

⇒
`2* 127^(\circ)+2* m\angle BCD=360^(\circ)`

⇒
`2( 127^(\circ)+m\angle BCD)=360^(\circ)`

⇒
`( 127^(\circ)+m\angle BCD)=180^(\circ)`

⇒
`m\angle BCD=53^(\circ)`

Now, the perimeter of a parallelogram= 2×sum of any two adjacent sides

2×(15)=30 unit