Question

NO LINKS!! URGENT HELP PLEASE!!

Use the parallelogram ABCD to find the following

8. part 1
a. DC=
c. m<DCB=
e. m<ABC= ​

Answer 1

a) DC = 16

c) m∠DCB = 120°

e) m∠ABC = 60°

Explanation:

Part a

The opposite sides of a parallelogram are equal in length. Therefore, DC is the same length as AB.

As AB = 16, then DC = 16.

`\hrulefill`

Part c

The opposite angles of a parallelogram are equal in measure. Therefore, m∠DCB is equal to m∠DAB.

As m∠DAB = 120°, then m∠DCB = 120°.

`\hrulefill`

Part e

Adjacent angles of a parallelogram sum to 180°. Therefore:

⇒ m∠ABC + m∠DAB = 180°

⇒ m∠ABC + 120° = 180°

⇒ m∠ABC + 120° - 120° = 180° - 120°

⇒ m∠ABC = 60°

Answer 2

a. 16

c. 120°

e. 60°

Explanation:

Properties of Parallelogram:

• Opposite sides are congruent.
• Opposite angles are congruent.
• Consecutive angles are supplementary.
• The diagonals bisect each other.
• The sum of the interior angles is 360 degrees.

For Question:

a.

DC= AB=16 Opposite side is congruent.

c.

m ∡DCB = m ∡DAB=120° Opposite angles are congruent.

e.

m ∡ABC= ​?

m ∡ABC+ m∡DAB =180° Consecutive angles are supplementary.

Substituting value

m ∡ABC + 120°=180°

m ∡ABC =180°-120°=60°

m ∡ABC=60°