Nancy is checking to determine if the expressions x+4+x and 6+2x-2 are equivalent. when x=3 , she correctly finds that both expressions have a value of 10. when x+4+x=14, she correctly evaluates the first expression to find

Expressions are equivalent.

Step-by-step explanation:

Expressions are said to be equivalent if same values are obtained on plugging same number in different expressions

for example

x+4+x at x =3  gives 3+4+3 = 10

6+2x-2 at x=3 gives 6+2(3)-2 = 6+6-2 = 10

therefore given expressions are equivalent.

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°