Question

Sum of the internal angles of a polygon is ${540}^o$
How many sides does it have?
If the angle are consecutive natural numbers. What is the measure of the smallest angles?

Answer 1

Let there are $n$ sides in the polygon that has a sum of internal angles ${540}^{\circ }$ then

$(n-2)\times {180}^{\circ }={540}^{\circ }$

$n-2=3$

$n=5$

It have $5$ sides so it is a pentagon.

Now, the angles are in consecutive order then

${540}^{\circ }÷5={108}^{\circ }$

So, ${106}^{\circ }+{107}^{\circ }+{108}^{\circ }+{109}^{\circ }+{110}^{\circ }={540}^{\circ }$

So, the smallest angle will ${106}^{\circ }.$

Hence, this is the answer.