In triangle ABC, angle A is 40 more than angle B, and angle C is 1/4 of their sum.

univerkov | April 18, 2021 | education

In order to find the values of all angles of a triangle ABC, one should recall the rule according to which the sum of the values of all angles of a triangle is equal to 180 °.
That is, A + B + C = 180 °.
Now let’s take the angle B as x degrees.
Then the angle A is x + 40 °.
So the angle C is (x + x + 40 °) / 4.
Now let’s compose and solve the equation.
x + x + 40 + (x + x + 40) / 4 = 180.
2x + 40 + (2x + 40) / 4 = 180.
2x + 40 + (2x: 4 + 40: 4) = 180.
2x + 40 + 0.5x + 10 = 180.
2.5x + 50 = 180.
2.5x = 180 – 50.
2.5x = 130.
x = 130: 2.5.
x = 52 ° – angle B.
x + 40 ° = 52 ° + 40 ° = 92 ° – angle value A.
Next, we find the value of the angle C.
(52 ° + 92 °) / 4 = 144 °: 4 = 36 ° – the value of the angle C.
Answer: A = 92 °; B = 52 °; C = 36 °.

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