Question

the angles of a pentagon are in the ratio of 2:3:6:7:9. find the angles​

Answer 1

Answer:

Step-by-step explanation:

A pentagon has 5 sides, and can be made from three triangles, So,its interior angles  3 × 180° = 540°

So 2x + 3x + 6x + 7x + 9x = 540

25x = 540

x = 540 / 25

x = 21.6

2x = 2 ( 21.6 ) =43.2

3x = 3 ( 21.6 ) =64.8

6x = 6 ( 21.6 ) =129.6

7x = 7 ( 21.6 ) =151.2

9x = 9 ( 21.6 ) =194.4

Answer 2

Answer:

$\huge \tt \: given$

• Angle of a Pentagon = 2:3:6:7:9

$\huge \tt \: to \: find$

Measure of each angle

$\huge \tt \: solution$

Let the angle be x.

As we know that sum of all sides of a Pentagon is 540⁰.

$\sf \mapsto \: 2x + 3x + 6x + 7x + 9x = 540$

$\sf \mapsto \: 27x = 540$

$\sf \mapsto \: x = \dfrac{540}{27}$

$\sf \mapsto \: x = 20 \degree$

$\huge \bf \: sides \: \downarrow$

$\sf \mapsto \: 2x = 2(20) = 40$

$\sf \mapsto \: 3x = 3(20) = 60$

$\sf \mapsto \: 6x = 6(20) = 120$

$\sf \mapsto \: 7x = 7(20) = 140$

$\sf \mapsto \: 9x = 9(20) = 180$

Let's verify

$\sf40 + 60 + 120 + 140 + 180 = 540$

$\sf \: 100 + 260 + 180 = 540$

$\sf \: 540 = 540$

LHS = RHS