ABCD parallelogram angle A is eight times less than the sum of angles B, C, D. Find the angles of a parallelogram.
September 14, 2021 | education
| 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 °
One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.