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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°


Team Careers360 1st Jan, 2024
Answer (1)
Team Careers360 23rd Jan, 2024

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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