Question : In $\triangle ABC$, M and N are the points on side BC such that AM $\perp$ BC, AN is the bisector of $\angle A$, and M lies between B and N. If $\angle B=68^{\circ}$, and $\angle \\{C}=26^{\circ}$, then the measure of $\angle MAN$ is:
Option 1: 21º
Option 2: 28º
Option 3: 24º
Option 4: 22º
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Correct Answer: 21º
Solution :
$\triangle$ABC, M and N are the side on BC such that AM $\perp$ BC, AN is the bisector $\angle$A, and M lies between B and N
$\angle$B = 68$^\circ$, and $\angle$C = 26$^\circ$
Concept used:
$\triangle$ABC, M and N are the sides on BC such that AM ⊥ BC, AN is the bisector $\angle$A, and M lies between B and N.
$\angle$MAN = $\frac{(\angle \text{B} - \angle \text{C})}{2}$
Solution:
⇒ $\angle$MAN = $\frac{(\angle \text{B} - \angle \text{C})}{2}$
⇒ $\angle$MAN = $\frac{(68^\circ - 26^\circ)}{2}$ = 21$^\circ$
Hence, the correct answer is 21$^\circ$.
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