Question

Two interior angles of a pentagon is $45°$and each of the other angles are in the ratio $3:4:5$. Find the angles.

Answer 1

Sum of interior angles of any polygon with number of sides $n$ is $\left(n-2\right)\times 180°$

So, for pentagon, $n=5$

So,

$$\begin{gathered} (5-2)\times 180° \\ 3\times 180°=540° \end{gathered}$$

Let the three angles be $3x,4x$and $5x$

So,

$$\begin{gathered} 45°+45°+3x+4x+5x=540° \\ 90°+12x=540° \\ 12x=540°-90° \\ 12x=450 \\ x=\frac{450}{12}=37.5 \end{gathered}$$

Hence, the angles are -

$$\begin{gathered} 3x=3\times 37.5=112.5° \\ 4x=4\times 37.5=150° \\ 5x=5\times 37.5=187.5° \end{gathered}$$