Answer:
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°.
