The sides of ΔDEF are d, e, and f. If the lengths of d = 12 and e = 19, what are the possible lengths of f?
Question 10 options:

A)

7 < f < 31

B)

12 < f < 31

C)

7 < f < 19

D)

12 < f < 19

the statemwnt is the company makes small and large snow cone cups.

large=it holds more then the small

small=it holds less then the large

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°

if x = 1, then the answer is 3.5