Question

The measures of the angles of a quadrilateral are in the ratio 3:4:5:6. Find their measures in radians.

Answer 1

Hello friend! Thanks for asking question, here is the answer.

Let the angles of the quadrilateral be 3k, 4k, 5k and 6k in degrees.
Since sum of the angles of the quadrilateral is 360°,
3k + 4k + 5k + 6k = 360°
18k = 360°
k = 20°

Therefore, the angles of the quadrilateral are

3k = 3 × 20= 60° = (60×pie/180) radian = (pie/3)radian

4k = 4 × 20= 80° = ( 80× pie/180) radian = (4pie/ 9) radian

5k = 5 × 20= 100° = ( 100 × pie/180) radian = (5pie/9) radian

6k = 6 × 20= 120° = (120 × pie/180) radian = ( 2pie/3) radian


Therefore, the measures of the angles in radians are pie/3, 4pie/9, 5pie/9 and 2pie/3.




Hope it helps.