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The sum of the measures of the angles of any triangle is 180 degrees . In a certain triangle, the largest angle measures 55 degrees less than twice the median angle, and the smallest angle measures 25 degrees less than the median angle find the measures of all three angles matrix

Respuesta :

Answer:

75, 65 and 40 degrees.

Step-by-step explanation:

Let the largest angle be x degrees, the median y and the smallest z.

x = 2y - 55

z = y - 25

x + y + z = 180

Substituting for x in the last equation:

2y - 55 + y + z = 180

3y + z = 235  

From the second equation:

- y + z = -25     Subtract this from the last equation:

4y = 260

y = 65 degrees

so z = 65 - 25 = 40 degrees.

- and x = 180 - 65 - 40 = 75 degrees,.

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