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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