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The Measure of the largest angle of a triangle is 40° more than the measures of the smallest angle, and the measures of the remaining angle is 20° more than the measure of the smallest angle. Find the measure of each angle.​

Respuesta :

Answer:

40, 60 and 80 degrees.

Step-by-step explanation:

Let the smallest angle be x degrees. Then:

The 3 angles are x, x + 40 and x + 20.

As there are 180 degrees in a triangle:

x + x + 40 + x + 20 = 180

3x = 180 -40--20 = 120

x = 40 degrees.

The other 2 angles are  60 and 80 degrees.

A = x + 40°, B = x, C = x + 20°

(x + 40°) + x + (x + 20°) = 180°

3x + 60° = 180°

3x = 180° - 60°

3x = 120°

x = 40°

B = 40°

A = 40° + 40° = 80°

C = 40° + 20° = 60°

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