Answer/Step-by-step explanation:
1. <ABC and <BCD are alternate interior angles. Alternate interior angles are equal, therefore, since m<ABC = 38°, then m<BCD = 38°
2. m<ECF = m<BCD (corresponding angles)
m<ECF = 38° (substitution)
3. m<DCF + m<ECF = 180° (linear pair)
m<DCF + 38° = 180° (substitution)
m<DCF = 180° - 38° (Subtraction property of equality)
m<DCF = 142°
The measure of the following angles are as follows;
∠BCD = 38°
∠ECF = 38°
∠DCF = 142°
When a transversal line cut across parallel lines, the angles form include corresponding angles, alternate angles etc.
Therefore,
∠BCD = 38 degrees(alternate angles)
∠ECF = 38 degrees(corresponding angles)
∠DCF = 180 - 38 = 142 degrees(angles on a straight line)
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