In the diagram below, de and ef are tangent to o. which equation could be solved to find x, the measure of df.

The answer to your question is letter D

Step-by-step explanation:

Formula

                     m∠E =

Data

m∠E = 48°

DGF = 228°

DF = x°

Substitution

                    48° =

Solution

                                     2(48) = 228 - x°

                                     96 = 228 - x°

                                     96 - 228 = - x°

                                    - 132 = - x°

                                       x° = 132°

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°