- Since AD || BC and AB || DC, quadrilateral ABCD is a parallelogram.
- In a parallelogram, opposite angles are equal. Therefore, m∠DCB = m∠DAB = 80°.
- Consecutive angles in a parallelogram are supplementary. Therefore, m∠ABC = 180° - m∠DAB = 180° - 80° = 100°.
- Similarly, m∠ADC = 180° - m∠DCB = 180° - 80° = 100°.
- Given m∠BDC = 60°, and since m∠ADC = 100°, then m∠ADB = m∠ADC - m∠BDC = 100° - 60° = 40°.
- Since AB || DC and BD is a transversal, alternate interior angles are equal: m∠ABD = m∠BDC = 60°.
- In triangle ABD, the sum of angles is 180°: m∠DAB + m∠ABD + m∠ADB = 80° + 60° + 40° = 180° (verified).
- Since AD || BC and BD is a transversal, alternate interior angles are equal: m∠DBC = m∠ADB = 40°.
- In triangle BDC, the sum of angles is 180°: m∠BDC + m∠DBC + m∠DCB = 60° + 40° + 80° = 180° (verified).
- Since E-B-F is a straight line, m∠EBD + m∠DBC = 180° (linear pair). Thus, m∠EBD = 180° - m∠DBC = 180° - 40° = 140°.
- Similarly, m∠FBC = 180° - m∠DBC = 180° - 40° = 140° (if FBC is considered as the angle on the other side, but typically FBC would be adjacent to DBC; assuming FBC is the angle between FB and BC, which is adjacent to DBC along the straight line, so m∠FBC = 180° - m∠DBC = 140°).
Final list of found angles:
- m∠DCB = 80°
- m∠ABC = 100°
- m∠ADC = 100°
- m∠ADB = 40°
- m∠ABD = 60°
- m∠DBC = 40°
- m∠EBD = 140°
- m∠FBC = 140°
Parent Tip: Review the logic above to help your child master the concept of angle puzzle worksheet answers.
