Question

type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar. polygon abcd is a parallelogram, and ( mangle abc = 127^{circ} ). the length of ( overline{bc} ) is 10 units, and the length of ( overline{ab} ) is 5 units. the perimeter of the parallelogram is units, and ( mangle bcd ) is ( ^{circ} ).

Explanation:

Step1: Calculate the perimeter of the parallelogram

In a parallelogram, opposite sides are equal. So \(AB = CD = 5\) units and \(BC=AD = 10\) units.
The perimeter \(P\) of a parallelogram is given by \(P = 2(AB + BC)\).
Substitute \(AB = 5\) and \(BC = 10\) into the formula:
\(P=2(5 + 10)=2\times15 = 30\)

Step2: Find the measure of \(\angle BCD\)

In a parallelogram, adjacent angles are supplementary. That is \(\angle ABC+\angle BCD = 180^{\circ}\)
Given \(\angle ABC = 127^{\circ}\), then \(\angle BCD=180^{\circ}-\angle ABC\)
\(\angle BCD = 180 - 127=53^{\circ}\)

Answer:

The perimeter of the parallelogram is \(30\) units, and \(m\angle BCD\) is \(53^{\circ}\)