Question

The four angles of a quadrilateral are in the ratio 7:4:5:2. Difference between the largest and the smallest angle is:
80 degree
40 degree
140 degree
100 degree​

Answer 1

Answer:-

Given:

The four angles of a quadrilateral are in the ratio 7 : 4 : 5 : 2

Let the angles be 7x , 4x , 5x , 2x.

We know that,

Sum of four angles of a quadrilateral = 360°

Hence,

7x + 4x + 5x + 2x = 360°

→ 18x = 360

→ x = 360/18

→ x = 20

Hence,

• 1st angle = 7(20) = 140°

• 2nd angle = 4(20) = 80°

• 3rd angle = 5(20) = 100°

• 4th angle = 2(20) = 40°

→ Largest angle = 140°

→ Smallest angle = 40°

Their difference = 140° - 40°

→ Difference between largest and Smallest angle = 100°.

Therefore, the difference between the largest and Smallest angle is 100°.

Answer 2

Answer:

here is your answer

Step-by-step explanation:

let all the given ratios be 7x , 4x , 5x and 2x respectively.

By angle sum property of a quadrilateral ,

<A + <B + <C + < D = 360°

7x + 4x + 5x + 2x = 360°

18x = 360°

x = 360° / 18

x = 20°

1st angle = 7x = 7 × 20° = 140°

2nd angle = 4x = 4 × 20° = 80°

3rd angle = 5x = 5 × 20° = 100°

4th angle = 2x = 2 × 20° = 40

The difference between the largest angle ( 7x ) and the smallest angle ( 2x ) is 100°.