Question

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Use the parallelogram ABCD to find the following.
8. part 2

b. AE=

d. m<DCB=

f. m<ADC= ​

Answer 1

b) AE = 7

d) m∠DCB = 120°

f) m∠ADC = 60°

Explanation:

Part b

The diagonals of a parallelogram always bisect each other.

Therefore, point E (the point of intersection of the two diagonals) is the midpoint of diagonal AC. So AE = EC.

As EC = 7, then AE = 7.

`\hrulefill`

Part d

As the measure of the opposite angles of a parallelogram are equal, then m∠DCB is equal to m∠DAB. From inspection of the given parallelogram, we can see that m∠DAB = 120°. Therefore:

m∠DCB = 120°

`\hrulefill`

Part f

Adjacent angles of a parallelogram are supplementary (sum to 180°).

Angle DAB and angle ADC are adjacent angles, so their sum is 180°.

Therefore:

⇒ m∠ADC + m∠DAB = 180°

⇒ m∠ADC + 120° = 180°

⇒ m∠ADC + 120° - 120° = 180° - 120°

⇒ m∠ADC = 60°

Answer 2

b. 7

d. 120°

f. 60°

Explanation:

The properties of a parallelogram are:

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

For Question:

b.

AE=CE=7 since diagonals of parallelogram bisect each other

d.

m ∡ DCB= m ∡DAB=120° Opposite angle in a parallelogram is congruent or equal.

f.

m ∡ ADC=?

Here

m ∡ADC+ m ∡DAB=180° being co interior angle

m ∡ADC+120°=180°

m ∡ADC=180°-120°=60°

m ∡ADC=60°