Question

ABCD is a llgm with angle A=80°, the internal bisecters of angle B and angle c meet at O . Find the measure of all the three angles of BCD​

Answer 1

Answer:

= it was BCO not BCD

=Angle OBC = 50°

=Angle OCB = 40°

=Angle BCO = 90°

Step-by-step explanation:

= In parallelogram ABCD

= Angle A = Angle C ...( Opposite angle of a || gm are equal )

= Angle B = Angle D ...( Opposite angle of a || gm are equal )

= Angle A = Angle C = 180°

= Angle A + Angle D = 180° ( Co- interior angle )

= 80° + Angle D = 180°

= Angle D = 180 °- 80°

= Angle D = 100

= Angle B = Angle D

= Angle B = 100

= Having on the both sides

= c/2 = 80/ 2

= Angle OBC = 50° ...( OB is the Angle bisects of Angle B )

= In Angle BOC

= Angle OBC + Angle OCB + Angle BOC = 180°

= 50°+ 40°+ Angle BOC = 180°

= 90° + Angle BOC = 180°

= Angle BOC = 180° - 90°

= 90°

hope it help

Answer 2

Step-by-step explanation:

∠A = 80°

We know that the opposite angles of a parallelogram are equal.

∠A = ∠C = 80°

And

∠OCB = (1/2) × ∠C

= (1/2) × 80°

= 40°

∠B = 180° – ∠A (the sum of interior angles on the same side of the transversal is 180)

= 180° – 80°

= 100°

Also,

∠CBO = (1/2) × ∠B

= (1/2) × 100°

= 50°

By the angle sum property of triangle BCO,

∠BOC + ∠OBC + ∠CBO = 180°

∠BOC = 180° – (∠OBC + CBO)

= 180° – (40° + 50°)

= 180° – 90°

= 90°

Hence, the measure of all the three angles of a triangle BCO is 40°, 50° and 90°......

Hope it's helps....♦️⚡