The measures of angles of a quadrilateral are in the ratio 2 3 6 7 find their measures in degrees and in radians?

Answer 1

The angles are:

40° = 2π/9 radians ≈ 0.698 radians,

60° = π/3 radians ≈ 1.047 radians

120° = 2π/3 radians ≈ 2.094 radians, and

140° = 7π/9 radians ≈ 2.443 radians.

There are 2 + 3 + 6 + 7 = 18 parts.

The sum of the angles in a quadrilateral are 360°

→ each part is 360° ÷ 18 = 20°

→ the angles are:

2 x 20° = 40°

3 x 20° = 60°

6 x 20° = 120°

7 x 20° = 140°

A full circle is 2π radians

→ 360° = 2π radians

→ 1° = π/180 radians

→ 40° = 40 x π/180 radians = 2π/9 radians ≈ 0.698 radians

→ 60° = 60 x π/180 radians = π/3 radians ≈ 1.047 radians

→ 120° = 120 x π/180 radians = 2π/3 radians ≈ 2.094 radians

→ 140° = 140 x π/180 radians = 7π/9 radians ≈ 2.443 radians