Question

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

Answer 1

Answer :

›»› The smaller angle of a quadrilateral is 40°.

Step-by-step explanation :

Given :

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

To Find :

• The smallest angle of a quadrilateral.

Knowledge required :

The sum of all four angles of a quadrilateral is 360°.

This statement is known as 'angle sum property of quadrilateral'.

Solution :

Let us assume that, the angles of a quadrilateral are 2x, 3x, 5x, 8x respectively

As we know that

The sum of all four angles of a quadrilateral is 360°.

→ 2x + 3x + 5x + 8x = 360

→ 5x + 5x + 8x = 360

→ 10x + 8x = 360

→ 18x = 360

→ x = 360/18

→ x = 20.

Therefore,

The all four angles of a quadrilateral will be,

• 2x = 2 * 20 = 40°.
• 3x = 3 * 20 = 60°.
• 5x = 5 * 20 = 100°.
• 8x = 8 * 20 = 160°.

Here we can conclude that the smallest angle of a quadrilateral will be 40°.

Hence, the smaller angle of a quadrilateral is 40°.

Answer 2

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

• 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°.