Question

9. The exterior angles of a pentagon are in the ratio 1: 2:3: 4:5. Find all the interior
angles of the pentagon.​

Answer 1

Given

Exterior angles of a Pentagon are in the ratio 1:2:3:4:5

To Find

All Interior angles of a Pentagon

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

Step by step explanation

We know that the sum of exterior angles of a Pentagon is equal to 360°.So, we just add all the given angles which are in the ratio and place to 360°.

According to the question

Let the first angle be x

second angle be 2x

third angle be 3x

fourth angle be 4x

fifth angle be 5x

Now,adding all

$\sf \longmapsto \: x + 2x + 3x + 4x + 5x = 360$

$\sf \longmapsto \: 15x = 360$

$\sf \longmapsto \: x = \dfrac{360}{15} = 24$

Therefore, x is 24°

Now ,finding all angles of pentagon

1. x=24°
2. 2x=2×24°=48°
3. 3x=3×24°=72°
4. 4x=4×24°=96°
5. 5x=5×24°=120°

We have to find Interior angles of pentagon

Then , interior angles of pentagon are :

➠180°-24°=156°

➠180°-48°=132°

➠180°-72°=108°

➠180°-96°=84°

➠180°-120°=60°