Question

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

Answer 1

Explanation:

let the common multiple for below be., x:3x : 4x : 2x : x : 2x : 3x : 2x

x+ 3x + 4x + 2x + x + 2x + 3x + 2x = 360°...( the sum of all exterior angles of a octagon).

X + X + X + X + X + X + X + X + 3 + 4 + 2 + 2 + 3 + 2 = 360°....( collection of like terms)

8X + 3 + 4 + 2 + 2 + 3 + 2 = 360°

8X + 16 = 360°

8X = 360°- 16 ...( transforming the unnecessary term from L.H.S. to R. H.S)

8X = 344°

X = 344°÷ 8....( 8 is a multiplier is L.H.S . so, it will become divisor in R.H.S )

X = 43.

Now,

considering the ratio.

1. 1× 43 = 43
2. 3 × 43= 129
3. 4 × 43= 172
4. 2 × 43= 86
5. 1 × 43= 43
6. 2 × 43= 86
7. 3 × 43= 129
8. 2 × 43= 86.