Question

1 ABCD is a parallelogram with ZA = 80°. The internal bisectors of ZB and C meet each other at O. Find the measure of the three angles of ABCO. D C С 80° А B
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Answer 1

Answer:

‹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°.