Question

Find the angles of trapezium when it's angles are in the ratio 2:3:7:8

Answer 1

Answer: 36°,54°,126° & 144°

Step-by-step explanation:

Let the angles be 2x, 3x, 7x and 8x.

According to the Angle Sum Property of quadrilaterals all angles add up to 360°

2x+3x+7x+8x=360°

20x=360°

x=18°

Angles-

2x=2×18=36°

3x=3×18=54°

7x=7×18=126°

8x=8×18=144°

Answer 2

Let the angles in the ratio 2 : 3 : 7 : 8 be 2x, 3x, 7x & 8x

Sum of all the angles of trapezium is 360°


According to the given condition,

2x + 3x + 7x + 8x = 360

∴ 20x = 360

∴ x = 18


∴ 1st angle ➾ 2x

➾ 2 × 18

➾ $\boxed{\boxed{\textsf{36\:degree}}}$


∴ 2nd angle ➾ 3x

➾ 3 × 18

➾ $\boxed{\boxed{\textsf{54\:degree}}}$


∴ 3rd angle ➾ 7x

➾ 7 × 18

➾ $\boxed{\boxed{\textsf{126\:degree}}}$


∴ 4th angle ➾ 8x

➾ 18 × 8

➾ $\boxed{\boxed{\textsf{144\:degree}}}$


Additional information :-

Trapezium is a type of quadrilateral. Therefore, we have considered the sum of all angles of trapezium as sum of all angles of a quadrilateral. If there are 2 right angles then the sum is 180°