Question : In a $\triangle \mathrm{XYZ}, \mathrm{XO}$ is the median and $\mathrm{XO}=\frac{1}{2} \mathrm{YZ}$. If $\angle \mathrm{YXO}=30^{\circ}$, then what is the value of $\angle \mathrm{XYZ}$?
Option 1: 15°
Option 2: 90°
Option 3: 30°
Option 4: 60°
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Correct Answer: 30°
Solution :
Since $XO$ is the median,
$YO = OZ = \frac{YZ}{2}$
Given $XO = \frac{YZ}{2}$,
⇒ $YO = XO$
⇒ $\triangle XYO$ is an isosceles triangle.
Given, $\angle YXO = 30°$
Since angles opposite to equal sides of an isosceles triangle are equal,
⇒ $\angle XYO = 30°$
⇒ $\angle XYZ = 30°$
Hence, the correct answer is 30°.
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