Q.The angles of a quadrilateral are in A.P. and the greatest angle is double the least. Find angles of the quadrilateral in radian.

Step 1: Let the angles be $a, a+d, a+2d, a+3d$ (A.P.). Sum: $4a+6d=360° \Rightarrow 2a+3d=180°$.

Step 2: Greatest $=2\times$ least: $a+3d=2a \Rightarrow 3d=a$.

Step 3: Substitute into $2a+3d=180°$: $2a+a=180° \Rightarrow 3a=180° \Rightarrow a=60°$, so $d=\frac{a}{3}=20°$.

Step 4: Angles: $60°, 80°, 100°, 120°$. Check: sum $=360°$ ✓, greatest $120°=2\times60°$ ✓. …

Write the four A.P. angles as a, a+d, a+2d, a+3d, use the 360° quadrilateral sum together with the 'greatest = 2×least' co …

• Using a triangle-style three-term A.P. (a−d, a, a+d) instead of the correct four-term form for a quadrilateral. …