Question : In a cyclic quadrilateral MNOP, $\angle$M is opposite to $\angle$O, If 2$\angle$O = 3$ \angle$M, then what is the value of $\angle$M?
Option 1: 88°
Option 2: 108°
Option 3: 72°
Option 4: 96°
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Correct Answer: 72°
Solution : In a cyclic quadrilateral, the sum of a pair of opposite angles is 180°. ⇒ $\angle$M + $\angle$O = 180° Given that 2$\angle$O = 3$ \angle$M, ⇒ $\angle$O = 1.5$ \angle$M Substituting this into the formula $\angle$M + $\angle$O = 180°, ⇒ $\angle$M + 1.5$\angle$M = 180° Solving this equation gives: ⇒ 2.5$\angle$M = 180° ⇒ $\angle$M = $\frac{180^\circ}{2.5}$ ⇒ $\angle$M = 72° Hence, the correct answer is 72°.
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