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in a certain triangle angle c is 40 degrees more than the sum of the measure of angle a and angle b. the measure of angle a is 20 degrees less than the measure of angle b. find the measure of each angle

Respuesta :

reinhard10158

Step-by-step explanation:

the sum of all angles in a triangle is always 180°.

angle c = angle a + angle b + 40

angle a = angle b - 20

angle a + angle b + angle c = 180

using the second equation in the first :

angle c = (angle b - 20) + angle b + 40 = 2×angle b + 20

using this and the second equation in the third equation :

(angle b - 20) + angle b + (2×angle b + 20) = 180

4×angle b = 180

angle b = 45°

angle a = angle b - 20 = 45 - 20 = 25°

angle c = angle a + angle b + 40 = 25 + 45 + 40 = 110°

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