ABCD parallelogram angle A is eight times less than the sum of angles B, C, D. Find the angles of a parallelogram.

1. ∠А is less than (∠В + ∠С + ∠Д) by 8 times according to the condition of the problem, that is, (∠В + ∠С + ∠Д) = 8∠А.

2. ∠А + ∠В + ∠С + ∠Д = 360 ° (according to the properties of a convex quadrilateral).

3. We replace in this expression (∠В + ∠С + ∠Д) by 8∠А:

∠А + 8∠А = 360 °.

9∠А = 360 °.

∠А = 40 °.

∠А + ∠В = 180 ° (according to the properties of the parallelogram).

∠В = 180 ° – ∠А = 180 ° – 40 ° = 140 °.

∠А = ∠С = 40 °, ∠В = ∠Д = 140 ° (the angles of the parallelogram opposite each other are equal).

Answer: ∠А = ∠С = 40 °, ∠В = ∠Д = 140 °




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