Question

the angles of pentagon are in the ratio 2:3:3:3:4. find the least angle of pentagon

Answer 1

Sum of interior angle in a pentagon

= (n-2) × 180°
= 5-2 × 180°
= 3×180°
= 540°

let the common factor be x

1st side = 2x
2nd side = 3x
3rd side = 3x
4th side = 3x
5th side = 4x

2x + 3x + 3x + 3x + 4x = 540

15x = 540

$x = \frac{540}{15}$
x = 36

it can be seen that

2x is the smallest angle

therefore

2 × 36° = 72 °

Answer 2

since sum of all angles of pentagon is 540
let each angle be 2x 3x 3x 3x 4x
then,
2x + 3x + 3x + 3x + 4x =540
15 x= 50

x = 540
-------- = 36*
15
therefore, least angle = 2×36 * =72*