The four angles of a quadrilateral are in the ratio 2 : 3 : 5 : 8. The...
Let the angles are 2x, 3x, 5x, 8x.
∴ 2x + 3x + 5x + 8x = 360°
⇒ 18x = 360° ⇒ x = 20°
2x = 2 × 20° = 40°; 3x = 3 × 20° = 60°
5x = 5 × 20° = 100°; 8x = 8 × 20° = 160°
Required difference = 160° - 40° = 120°.
The four angles of a quadrilateral are in the ratio 2 : 3 : 5 : 8. The...
Let the angles of the quadrilateral be 2x, 3x, 5x, and 8x.
The sum of the angles of a quadrilateral is 360 degrees, so we have the equation:
2x + 3x + 5x + 8x = 360
18x = 360
x = 20
The largest angle is 8x = 8(20) = 160 degrees.
The smallest angle is 2x = 2(20) = 40 degrees.
The difference between the largest and smallest angles is 160 - 40 = 120 degrees.
Therefore, the difference between the largest and smallest angle of the quadrilateral is 120 degrees.