Question

Find the measure of each angle if the measure of three angles of a triangle are three consecutive natural numbers.

Answer 1

Let the three consecutive natural numbers be $x,x+1andx+2$.

By the angle sum property of the triangle, the sum of all the angles will always be equal to $180°.$

Now according to the question,

$$\begin{gathered} x+x+1+x+2=180° \\ 3x+3=180° \\ 3x=180°-3 \\ x=177°÷3 \\ x=59° \end{gathered}$$

The angles of the triangle are -

$$\begin{gathered} x=59° \\ x+1=59°+1=60° \\ x+2=59°+2=61° \end{gathered}$$

Hence, the angles of triangle are $59°,60°$ and $61°$.