Question

The measures of the angles of a triangle are 3 consecutive even integers. Find the measure of each angle.

Answer 1

58° , 60° , 62°

Explanation:

the sum of the 3 angles in a triangle = 180°

let the 3 consecutive even integers be n, n + 2, n + 4 , then

n + n + 2 + n + 4 = 180

3n + 6 = 180 ( subtract 6 from both sides )

3n = 174 ( divide both sides by 3 )

n = 58

n + 2 = 58 + 2 = 60

n + 4 = 58 + 4 = 62

the 3 angles are 58° , 60° , 62°

Answer 2

Given:

The angles of a triangle are as shown in the sketch below;

Consecutive even integers are the set of integers such that each integer in the set differs from the previous integer by a difference of 2 and each integer is divisible by 2.

For the three angles to be consecutive even integers, then

`\begin{gathered} x,y,z\text{ are consecutive even integers.} \\ \text{Hence,} \\ y-x=2 \\ y=x+2\ldots\ldots\ldots\ldots\ldots(1) \\ \\ \text{Also,} \\ z-y=2 \\ z=y+2 \\ z=x+2+2 \\ z=x+4\ldots.\ldots\ldots\ldots\ldots\ldots.\mathrm{}(2) \end{gathered}`

Since the three angles are in the triangle, then;

`\begin{gathered} x+y+z=180^0\ldots\ldots\ldots\ldots\ldots\ldots\ldots\text{.(the sum of angles in a triangle)} \\ \\ \\ \text{Substituting equation (1) and (2) into the equation above,} \\ x+(x+2)+(x+4)=180^0 \\ \text{Collecting the like terms,} \\ x+x+x+2+4=180^0 \\ 3x+6=180^0 \\ 3x=180-6 \\ 3x=174 \\ \text{Dividing both sides by 3,} \\ x=(174)/(3) \\ x=58^0 \end{gathered}`

Substituting the value of x into equations (1) and (2) to get the values of y and z,

`\begin{gathered} y=x+2 \\ y=58+2 \\ y=60^0 \\ \\ \text{Also,} \\ z=x+4 \\ z=58+4 \\ z=62^0 \end{gathered}`

Therefore, the measure of each angle if the angles are consecutive even integers are;

`58^0,60^0,62^0`