Quadrilateral ABCD is a parallelogram. DE = 6.1 cm and m∠DAB = 120°. What is BC? cm What is m∠BCD? ° What is AB? cm What is EB? cm

1) Opposite sides are congruent (AB = DC and AD=BC).
2) Opposite angles are congruent (D = B and A=C)
3) Consecutive angles are supplementary (A + D = 180° and D+C= 180°).
4) If one angle is right, then all angles are right.
5) The diagonals of a parallelogram bisect each other.
6) Each diagonal of a parallelogram separates it into two congruent triangles.

Part 1) What is BC?
BC=AD-----------> BC=10 cm--------> by Opposite sides are congruent

the answer Part 1) is
BC=10 cm

Part 2) What is m∠BCD?
m∠BCD=m∠DAB-----> m∠BCD=120°----> by Opposite angles are congruent

the answer part 2) is
m∠BCD=120°

part 3) What is AB?
AB=CD------> AB=5 cm----> by Opposite sides are congruent

the answer Part 3) is
AB=5 cm

Part 4) What is EB?
EB=DE-----> EB=6.1 cm----> by The diagonals of a parallelogram bisect each other.

the answer Part 4) is
EB=6.1 cm

abidemiokin abidemiokin · Answer 2 · 2021-11-29T13:28:19+01:00

The measure of BE is 4.33 cm

The measure of AB is 5 cm

For a parallelogram, the measure of its opposite sides are equal, hence;

AB = CD and

AD = BC

Similarly, the measure of the adjacent angles is supplementary;

m,C + m<D = 180

From the given diagram, m<BCD = 120 degrees

From the given diagram, we can see that CD = 5cm and since AB = CD, hence the measure of AB is 5cm

To get the measure of BE, we will use the sine rule on triangle BCD

BD/sin 120 = CD/sin 30

BD/sin120 = 2(5)

BD = 10sin120

BD = 8.660

From the diagram, BD = 2BE

BE = BD/2

BE = 8.66/2

BE = 4.33

Hence the measure of BE is 4.33 cm

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