Which expression illustrates the associative property of addition?
(3 + 19) – 12 = (3 + 12) - 19
O 3 + (19 - 12) = 3 + (19 + 12)
(3 + 19) – 12 = 3 + (19 - 12)
o 3+ (19 - 12) = 3 - (19 + 12)

Solution:

The associative property of addition of three numbers a, b and c is given as:

Option A

( 3 + 19 ) - 12 = (3 + 12) - 19

Here, +19 in left side of equation is written as -19 in right side of equation

Therefore, it does not represent associative property of addition

Option B

3 + (19 - 12) = 3 + (19 + 12)

Here, -12 in left side of equation is written as +12 in right side of equation

Therefore, it does not represent associative property of addition

Option C

(3 + 19) - 12 = 3 + (19 - 12)

22 - 12 = 3 + 7

10 = 10

This represents associative property of addition

Option D

3 + (19 - 12) = 3 - (19 + 12)

3 + 7 =  3 - 7

10 not equal to -4

Therefore, it does not represent associative property of addition

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°