JAMB Mathematics 2010 Paper

Concept:In a cyclic quadrilateral, opposite angles are supplementary, meaning their sum is $180^\circ$.Explanation:From the cyclic quadrilateral $TUVW$, identify the pair of opposite angles given in the diagram.Let the two opposite angles be $88^\circ$ and $(3x + 20)^\circ$.Apply the cyclic quadrilateral property:$$(3x + 20)^\circ + 88^\circ = 180^\circ$$Add the constants:$$3x + 108 = 180$$Subtract $108$ from both sides:$$3x = 180 - 108$$$$3x = 72$$Divide both sides by $3$:$$x = \frac{72}{3}$$$$x = 24$$Thus, the value of $x$ is $24^\circ$.Answer:$x = 24^\circ$, which is Option B.