The diagonals AC and BD of a parallelogram ABCD intersect each other at the point O. If DAC = 32° and AOB = 70°, then DBC is equal to


Given: AOB = 70°

DAC = 32°



AD BC and AC is transversal


ACB = 32°


Now,


AOB + BOC = 180°


70° + BOC = 180°


⇒ ∠BOC = 180° - 70°


⇒ ∠BOC = 110°


Sum of all angles of a triangle = 180°


⇒ ∠BOC + BCO + OBC = 180°


110° + 32°+ OBC = 180°


142°+ OBC = 180°


⇒ ∠OBC = 180° - 142°


⇒ ∠OBC = 38°


Hence, DBC = 38°

12
1