Question

The exterior angles of an octagon are in the ratio of 1;3:4:2:1:2:3: 2. Find all the interior angles of octagon​

Answer 1

Let 1st angle = x

2nd angle = 3x

3rd angle = 4x

4th angle = 2x

5th angle = x

6th angle = 2x

7th angle = 3x

8th angle = 2x

Sum of angle in octagon = 360°

$\bf According \: to \: Question :$

$x + 3x + 4x + 2x + x + 2x + 3x + 2x = 360 \\ \\ 18x = 360 \\ \\ x = \frac{360}{18} \\ \\ \large\boxed{ \green {\bf x = 20}}$

1st angle = 20°

2nd angle = 60°

3rd angle = 80°

4th angle = 40°

5th angle = 20°

6th angle = 40°

7th angle = 60°

8th angle = 40°

Answer 2

✯✯ QUESTION ✯✯

The exterior angles of an octagon are in the ratio of 1:3:4:2:1:2:3: 2. Find all the interior angles of octagon..

━━━━━━━━━━━━━━━━━━━━

$⇢Let\:1st\:Angle=1x$

$⇢Let\:2nd\:Angle=3x$

$⇢Let\:3rd\:Angle=4x$

$⇢Let\:4th\:Angle=2x$

$⇢Let\:5th\:Angle=1x$

$⇢Let\:6th\:Angle=2x$

$⇢Let\:6th\:Angle=3x$

$⇢Let\:8th\:Angle=2x$

➜Total sum of angles of an Octagon=360°

☛A.T.Q : -

$⇢1x+3x+4x+2x+1x+2x+3x+2x=360$

$⇢18x=360$

$⇢x=\cancel\dfrac{360}{18}$

☛$\large{\boxed{\bold{\bold{\red{\sf{x=20}}}}}}$

_______________________

• 1st Angle =1(20)=20°
• 2nd Angle=3(20)=60°
• 3rd Angle=4(20)=80°
• 4th Angle=2(20)=40°
• 5th Angle=1(20)=20°
• 6th Angle=2(20)=40°
• 7th Angle=3(20)=60°
• 8th Angle=2(20)=40°

_______________________