Question

The measures of angle of a quadrilateral are in the ratio 2:3:6:7.Find their measures in degrees and 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

Answer 2

Given:

The measures of the angles of a quadrilateral are in the ratio 2:3:6:7.

To find:

Their measures in degrees and radians.

Solution:

We can solve the above mathematical problem using the following mathematical approach.

Let the measures of the angles of the quadrilateral be 2x, 3x, 7x, and 6x.

We know that, the sum of all the angles in a quadrilateral is 360°.

$2x + 3x + 7x + 6x = 360^\circ\\\\18x = 360^\circ\\\\x = 20^\circ\\\\ The measures of the angles of quadrilateral are: \\2x = 2 \times 20^\circ = 40^\circ \\3x = 3 \times 20^\circ = 60^\circ \\7x = 7 \times 20^\circ = 140^\circ \\6x = 6 \times 20^\circ= 120^\circ$

Measures of the angles in radians:

$40^\circ = 2\pi/9 radians,\\60^\circ = \pi/3 radians,\\120^\circ = 2\pi/3 radians, and\\140^\circ = 7\pi/9 radians.$

Therefore, the measures in degrees and radians are 40°, 60°, 120°, 140°, and 2π/9 radians, π/3 radians, 2π/3 radians, 7π/9 radians respectively.