The angles of a triangle are consecutive even integers. Find the measure of each angle.

Expert Answers

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Let the smallest angle =  x

Then the second angle  = x+2

The third angle = x+4

But we know that the sum of the angles of a traingle = 180

Then,

x + (x+2) + (x+4) = 180

==> 3x + 6 = 180

==> 3x = 180- 6 = 174

Now divide by 3:

==> x= 174/3 = 58

Then the angles of the triangle are:

58 , 60, and 62.

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To answer this question, remember that the angles of a triangle always sum to 180 degrees. Let the three angles in question be labeled A, B, and C. Also, let A = n;

A = n; B = n + 2; C = n + 4;   i.e. consecutive even numbers.

A + B + C = n + n + 2 + n + 4 = 180

3n + 6 = 180

n = 174/3 = 58

Thus,

A = 58,

B= 60,

C = 62

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