It is known that the sum of the angles of any triangle is 180 degrees. Find angle A in triangle ABC

It is known that the sum of the angles of any triangle is 180 degrees. Find angle A in triangle ABC if: 1) Angle B is 2/3 and angle C is 1/5 of the sum of all the angles of the triangle 2) Angle A is 5/6 of angle B and angle C = 70 degrees

To solve problems, we use the theorem on the sum of angles in a triangle, and the rule for calculating a fraction of a number:

1) Find the angle B, B = 2/3 * 180 ° = 180 °: 3 * 2 = 120 °,

2) Angle C = 180 ° * 1/5 = 36 °,

3) 180 ° – (120 ° + 36 °) = 180 ° – 156 ° = 24 °.

Answer: angle A = 24 °.

Angle B = 180 ° – (angle A + angle C) = 180 ° – (angle A + 70 °) = 180 ° – 70 ° – angle A = 110 ° – angle A.
Let’s make the equation: angle B = x cm, angle A = 5/6 angle B, angle A = 5/6 x, angle C = 70 °.

x + 5/6 x + 70 ° = 180 °

15 / 6x = 180 ° – 70 °

11/6 x = 110 °

x = 110 °: 11/6

x = 110 ° * 6: 11 = 60 °, so the angle B = 60 °.

Answer: angle B = 60 °,

angle A = 180 ° – 60 ° – 70 ° = 50 °

Answer: angle A = 50 °.