JAMB Mathematics 2021 Paper

Concept:The sum of the interior angles of a quadrilateral is always $360^\circ$.Find the value of $x$ first, then substitute it into each angle expression to identify the smallest angle.Explanation:Write the sum of the four angles as an equation:$$(5x - 30) + (4x + 60) + (60 - x) + (3x + 61) = 360^\circ$$Collect like terms:$$11x + 151 = 360$$Subtract $151$ from both sides:$$11x = 209$$Divide both sides by $11$:$$x = 19$$Now substitute $x = 19$ into each angle expression:$5x - 30 = 5(19) - 30 = 65^\circ$$4x + 60 = 4(19) + 60 = 136^\circ$$60 - x = 60 - 19 = 41^\circ$$3x + 61 = 3(19) + 61 = 118^\circ$The smallest value among these angles is $41^\circ$.Answer:The smallest of these angles is $41^\circ$, which is obtained from $60 - x$.Therefore, the correct option is C.