Question

4. The angles of a quadrilateral are in the ratio
2:3:5:8. The smallest angle is​

Answer 1

$\Large\bf{\color{indigo}GiVeN,}$

The angles of a quadrilateral are in the ratio 2 : 3 : 5 : 8.

$\Large\bf\pink{Let,}$

The angles of the quadrilateral are 2x, 3x, 5x & 8x.

$\bf\red{We\:know\:that,}$

☆ The sum of angles of a quadrilateral = 360°

$\longmapsto\:\:\bf{2x\:+\:3x\:+\:5x\:+\:8x\:=\:360°\:}$

$\longmapsto\:\:\bf{18x\:=\:360°\:}$

$\longmapsto\:\:\bf{x\:=\:\dfrac{360}{18}\:}$

$\longmapsto\:\:\bf\green{x\:=\:20\:}$

$\Large\bf\orange{Therefore,}$

✒ The angles of the quadrilateral are,

=》 2x = (2 × 20) = 40°

=》 3x = (3 × 20) = 60°

=》 5x = (5 × 20) = 100°

=》 8x = (8 × 20) = 160°

$\Large\bold\therefore$ The smallest angle of the quadrilateral is 40°.

Answer 2

Given :-

The angles of a quadrilateral are in the ratio 2 : 3 : 5 : 8.

Let :-

The angles of the quadrilateral are 2x, 3x, 5x & 8x.

We know that :-

The sum of angles of a quadrilateral = 360°

⟼2x+3x+5x+8x=360°

⟼18x=360°

⟼ x = 20

Therefore :-

✒ The angles of the quadrilateral are,

=》 2x = (2 × 20) = 40°

=》 3x = (3 × 20) = 60°

=》 5x = (5 × 20) = 100°

=》 8x = (8 × 20) = 160°

∴ The smallest angle of the quadrilateral is 40°.