MB and NB are bisectors of $∠ C B A$ and $∠ A B D$ respectively. Find the value of $∠ M B N$ (in degrees).
90

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Solution

The correct option is A 90
$MB bisects ∠ C B A and NB bisects ∠ A B D .$

$So, ∠ A B M = \frac{1}{2} ∠ C B A and ∠ A B N = \frac{1}{2} ∠ A B D .$

$Now, ∠ M B N = ∠ A B M + ∠ A B N ∠ M B N = \frac{1}{2} ∠ C B A + \frac{1}{2} ∠ A B D ∠ M B N = \frac{1}{2} (∠ C B A + ∠ A B D) ∠ M B N = \frac{1}{2} ∠ C B D ∠ M B N = \frac{1}{2} \times 180^{\circ} ∠ M B N = 90^{\circ}$

$Therefore, the value of ∠ M B N is 90^{\circ} .$

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