Answer:
The measure of ∠BCD = (68.5)°
Step-by-step explanation:
Here, given:
AB II CD, BC II AE, ∠ABD = (3x +4)°, ∠BCD = (6x -8)° and ∠EDF = (7x-20)°
Now, as given
∠ABD = (3x +4)°
⇒∠BDC = (3x +4)° ( as AB II CD, PAIR OF ALTERNATE ANGLES) ... (1)
and , ∠EDF = (7x-20)°
⇒∠ADB = (7x-20)° (PAIR OF VERTICALLY OPPOSITE ANGLES)
⇒∠DBC = (7x-20)° ( as BC II AE, PAIR OF ALTERNATE ANGLES) ... (2)
Now, in Δ DBC:
∠BDC + ∠DBC + ∠BCD = 180° ( ANGLE SUM PROPERTY of a Δ)
⇒ (3x +4)° + (7x-20)° + (6x -8)° = 180
or, 16 x - 24 = 180
or, 16 x = 204
x = 204/16 = 12.75 , or x = 12.75
⇒ ∠BCD = (6x -8)° = 6(12.75) - 8 = 68.5
Hence, the measure of ∠BCD = (68.5)°
