Question -
Answer -
Let the angles of quadrilateral be (a – 3d)°, (a – d) °, (a + d) ° and (a + 3d) °.
We know that, thesum of angles of a quadrilateral is 360°.
a – 3d + a – d + a +d + a + 3d = 360°
4a = 360°
a = 360/4
= 90°
Given:
The greatest angle =120°
a + 3d = 120°
90° + 3d = 120°
3d = 120° – 90°
3d = 30°
d = 30°/3
= 10o
∴The angles are:
(a – 3d) ° = 90° –30° = 60°
(a – d) ° = 90° –10° = 80°
(a + d) ° = 90° +10° = 100°
(a + 3d) ° = 120°
Angles of quadrilateral in radians:
(60 × π/180) rad =π/3
(80 × π/180) rad = 4π/9
(100 × π/180) rad =5π/9
(120 × π/180) rad = 2π/3