Find the angle C of the triangle ABC if you know that the angle A is 20 degrees less than the angle B

| January 15, 2021 | education

Find the angle C of the triangle ABC if you know that the angle A is 20 degrees less than the angle B and 60 degrees less than the outer angle at the vertex C.

1. ∠О – external angle at vertex С.
2. ∠А is less than ∠В by 20 ° according to the condition of the problem, that is ∠В = ∠А + 20 °.
3. ∠А is less than О by 60 ° according to the problem statement, that is ∠О = ∠А + 60 °.
4. According to the properties of a triangle, the outer angle of a triangle is equal to the total value of the angles not adjacent to it:
∠О = ∠А + ∠В.
5. We replace ∠О by ∠А + 60 °, ∠В by ∠А + 20 °:
∠А + 60 ° = ∠А + ∠А + 20 °.
∠А = 60 ° – 20 ° = 40 °.
∠В = ∠А + 20 ° = 40 ° + 20 ° = 60 °.
6.∠С = 180 ° – ∠А – ∠В = 180 – 40 ° – 60 ° = 80 °.
Answer: ∠С is equal to 80 °.



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