Q.The measures of the angles of a triangle are in A.P. and the greatest is 5 times the smallest (least). Find the angles in degree and radian.

Step 1: Let the angles be $a-d, a, a+d$ (A.P.). Sum: $3a=180° \Rightarrow a=60°$.

Step 2: Greatest $= 5\times$ smallest: $a+d = 5(a-d) \Rightarrow a+d = 5a-5d \Rightarrow 6d = 4a \Rightarrow d = \frac{2a}{3} = \frac{2(60°)}{3} = 40°$.

Step 3: Angles: $a-d = 60°-40°=20°$, $a=60°$, $a+d=60°+40°=100°$. Check: greatest $100° = 5\times20°$ ✓, sum $=180°$ ✓. …

Write the three A.P. angles as a−d, a, a+d, use the 180° sum to find a, th …

• Setting up the ratio condition backwards (smallest = 5×greatest). …