It is known that the sum of the angles of any triangle is 180 °. Find ∠A in triangle ABC if: a) ∠B = 75 °, ∠C = 80 °

| August 18, 2021 | education

It is known that the sum of the angles of any triangle is 180 °. Find ∠A in triangle ABC if: a) ∠B = 75 °, ∠C = 80 °; b) ∠A is more than ∠B by 20 ° and less than ∠C by 40 °

a) By the condition of the problem, we know the values of the two angles of the triangle. Accordingly, to find the value of the third angle A, it is necessary to subtract the values of the known angles from 180 °:

∠А = 180 ° – 75 ° – 80 ° = 25 °.

b) Let us express the values of ∠В and ∠С through А: ∠В = ∠А – 40 °, ∠С = ∠А + 40 °.

And we will express the value of ∠А through the formula for the sum of the angles of a triangle: ∠А = 180 ° – ∠В – ∠С.

Substitute the values of the catch ∠В and ∠С, expressed in terms of А, and perform the calculations:

∠А = 180 ° – (∠А – 40 °) – (∠А + 40 °) = 180 ° – ∠А + 40 ° – ∠А – 40 ° = 180 ° – 2 * ∠А =>

3 * ∠А = 180 ° => ∠А = 60 °.



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