Answer:
1. BC = 25
2. m∠EDC = 125°
3) BD = 22
4) m∠EBD = 67°
5) FC = 17
6) m∠BEC = 24°
7) CD = 16
8) m∠DBC = 58°
Step-by-step explanation:
The dimensions of parallelogram EBCD are;
EB = 16, ED = 25, BF = 11, EC = 34, m∠BED = 55°, m∠CDB = 67°
1. BC = ED = 25 Opposite sides of a parallelogram are equal
2. m∠BCD = m∠BED = 55 opposite angles of a parallelogram are equal
m∠BCD + mEDC = 180° adjacent sides of a parallelogram are supplementary
m∠EDC = 180° - m∠BCD
∴ m∠EDC = 180° - 55° = 125°
m∠EDC = 125°
3) BD = BF × 2 Diagonals of a parallelogram bisect each other
∴ BD = 11 × 2 = 22
BD = 22
4) m∠EBD = m∠CDB = 67° from alternate angles between parallel lines
5) FC = EC/2 from diagonals of a parallelogram bisect each other
∴ FC = EC/2 = 34/2 = 17
FC = 17
6) m∠BEC = m∠BCE = 24° Alternate angles between parallel lines
m∠BEC = 24°
7) CD = EB = 16 Opposite sides of a parallelogram are equal
8) m∠EBC = m∠EDC = 125° from opposite angles of a parallelogram are equal
m∠DBC + m∠EBD = m∠EBC from angle addition postulate
∴ m∠DBC = m∠EBC - m∠EBD
m∠DBC = 125° - 67° = 58°
m∠DBC = 58°
