Question

The angles of a quadrilateral are in the ratio 1:2:8:9. Find the measures of its angles.​

Answer 1

Question -

The angles of a quadrilateral are in the ratio 1:2:8:9. Find the measures of its angles.

Solution -

let the angles be 1x, 2x, 8x and 9x. (x taken as the proportionality constant)

Therefore,

1x + 2x + 8x + 9x = 360°

=> 20x = 360°

=> x = $\dfrac{360 \degree}{20}$

=> x = 18°

Thus,

1. angle = 1(18°) = 18°
2. angle = 2(18°) = 36°
3. angle = 8(18°) = 144°
4. angle = 9(18°) = 162°

Answer 2

Answer:

Let x be proportionally constant

therefore, the angles will be 1x, 2x, 8x & 9x

So, by angle sum property of a quadrilateral

1x + 2x + 8x + 9x = 360°

=> 20x = 360°

=> x = 360°/20

=> x = 18°

hence, the angles will be

1x = 1 × 18 = 18°

2x = 2 × 18 = 36°

8x = 8 × 18 = 144°

9x = 9 × 18 = 162°