In the parallelogram ABCD, the angle A is 2 times less than the angle B. Determine all the angles of the parallelogram.
March 31, 2021 | education
| 1. Let us denote the angle by the symbol ∠.
2. Since ∠А is twice less than В according to the problem statement, ∠В = 2 .А.
3. According to the properties of the parallelogram, the total value of the angles adjacent to one and its sides is equal to 180 °.
4. With this in mind, we compose the following expression:
∠А + ∠В = 180 °. Replace ∠B with 2∠A:
∠А + 2∠А = 180 °.
3∠A = 180 °.
∠А = 60 °.
∠B = 2 x ∠A = 2 x 60 ° = 120 °.
5. Opposite angles of a parallelogram are equal (according to its properties):
∠С = ∠А = 60 °.
∠D = ∠В = 120 °.
Answer: ∠С = ∠А = 60 °, ∠Д = ∠В = 120 °.
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