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The sum of the angle measures of any triangle is 180°. Find each of the angle measure of a triangle if the second angle measure 10º more than twice the first, and the third angle measures 10° more
than the second.

Sagot :

Aayu0302idn

Answer:

26,72,82

Step-by-step explanation:

This question is solved by a system of equations. We have that:

x is the first angle.

y is the second angle.

z is the third angle.

The sum of the measures of the angles of a triangle is 180.

This means that, x + y + z = 180 -> Eq 1

Now,

The second angle measure 10º more than twice the first,

=> y = 2(x + 10) = 2x + 20

The third angle measures 10° more  than the second,

=> z = y + 10 = 2(x + 10) + 10 = 2x + 20 + 10 = 2x + 30

Equation(Substituting values in Eq 1) :-

=> x + (2x + 20) + (2x + 30) = 180

=> x + 2x + 20 + 2x + 30 = 180

=> x + 2x + 2x + 20 + 30 = 180

=> 5x + 50 = 180

=> 5x = 130

=> x = 26

Therefore,

x = 26

y = 2(26) + 20 = 72

z = 2(26) + 30 = 82

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