Question

the measures of the angles of a triangle are three consecutive even integers. find the measure of each angle. the angles measure , , and . (simplify your answers. do not include the degree symbol in your answers. use ascending order.)

Explanation:

Step1: Let the angles

Let the first even - integer angle be $x$. Then the next consecutive even - integer angles are $x + 2$ and $x+4$.

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$. So, $x+(x + 2)+(x + 4)=180$.

Step3: Simplify the left - hand side

Combine like terms: $3x+6 = 180$.

Step4: Solve for $x$

Subtract 6 from both sides: $3x=180 - 6=174$. Then divide both sides by 3: $x=\frac{174}{3}=58$.

Step5: Find the other angles

The second angle is $x + 2=58+2 = 60$. The third angle is $x + 4=58+4 = 62$.

Answer:

58, 60, 62