Question

1. if m∠dcf = 82°, m∠ecg = 61°, and m∠dce = 19°, what is the m∠fcg?

Explanation:

Step1: Find m∠ECF

We know that m∠DCF = 82° and m∠DCE = 19°. Since ∠DCF=∠DCE + ∠ECF, then ∠ECF=∠DCF - ∠DCE.
m∠ECF = 82°- 19°=63°

Step2: Find m∠FCG

We know that m∠ECG = 61° and we just found m∠ECF = 63°. Since ∠ECG=∠ECF+∠FCG, then ∠FCG=∠ECG - ∠ECF.
m∠FCG = 61° - 63°=- 2°. But angles can't be negative, there might be a mis - label or wrong data. Assuming the correct relationship and using the fact that we should consider the non - negative value of the angular difference, if we assume the correct formula based on the geometric arrangement is ∠FCG=∠ECF - ∠ECG.
m∠FCG=63° - 61° = 2°

Answer:

2°