Find the value of x in each case. RIGHT ANSWER GETS BRAINLIEST!

x= 19.5

Step-by-step explanation:

Angle G E B is  supplementary so we subtract 180 - 78 to find the unknown. which is 102. Then we subtract 102 from 180 giving 78. Since it asks for 4x, we divide 78 by 4, Equaling 19.5.

x = 23

Step-by-step explanation:

To find the value of x, we need the angle measure of ∠GEC.

The given angle measures are:

• ∠FGI = 14°

• ∠EGC = 78°

Based on the vertical angles theorem, ∠CGH = 14°.

Based on the alternate interior angles theorem, ∠ECG must also = 14°.

Now that 2 angles of ΔGEC are known, the missing value can be solved for:

180 - 78 - 14 = ?

180 - 92 = 88°

Because ∠BEC and ∠GEC are a linear pair, their angles are supplementary:

4x + 88 = 180   Subtract 88 from both sides to isolate x

4x = 92             Divide both sides by 4 to find the value of x.

x = 23

The value of x is 23°.