Question

Polygon ABCD is a parallelogram, and lass="latex-formula">∠$ABC$. 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,

$m\angle ABC+m\angle CDA+m\angle BAC+m\angle BCD=360^{\circ}$

⇒$2\times m\angle ABC+2\times m\angle BCD=360^{\circ}$

⇒$2\times 127^{\circ}+2\times m\angle BCD=360^{\circ}$

⇒$2( 127^{\circ}+m\angle BCD)=360^{\circ}$

⇒$( 127^{\circ}+m\angle BCD)=180^{\circ}$

⇒$m\angle BCD=53^{\circ}$

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

2×(15)=30 unit