![Polygon ABCD is a parallelogram, and [tex]m[/tex]∠[tex]ABC[/tex]. The length of is 10 units, and the length of is 5 units. The perimeter of the parallelogram is class=](https://us-static.z-dn.net/files/d29/ad62dd2eca75a91cda31eede1dce0e19.png)
Answer:The perimeter is [tex]30[/tex] unit and [tex]m\angle BCD=53^{\circ}[/tex]
Explanation: Since, here ABCD is a parallelogram in which, [tex]m\angle ABC=127^{\circ}[/tex] 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,
[tex]m\angle ABC=m\angle CDA[/tex] and [tex]m\angle BAC=m\angle BCD[/tex]
Moreover, we know that the sum of all angles of a parallelogram is [tex]360^{\circ}[/tex]
Thus,
[tex]m\angle ABC+m\angle CDA+m\angle BAC+m\angle BCD=360^{\circ}[/tex]
⇒[tex]2\times m\angle ABC+2\times m\angle BCD=360^{\circ}[/tex]
⇒[tex]2\times 127^{\circ}+2\times m\angle BCD=360^{\circ}[/tex]
⇒[tex]2( 127^{\circ}+m\angle BCD)=360^{\circ}[/tex]
⇒[tex]( 127^{\circ}+m\angle BCD)=180^{\circ}[/tex]
⇒[tex]m\angle BCD=53^{\circ}[/tex]
Now, the perimeter of a parallelogram= 2×sum of any two adjacent sides
2×(15)=30 unit
