In a ΔXYZ, XO is the median and $XO - \frac{1}{2}YZ$. If ∠YXO = 30°, then what is the value of ∠XYZ?

30°

According to the question,

in triangle XOY,

As XO is median, So 

⇒ YO = OZ

⇒ and as XO = \(\frac{1}{2}\) YZ, then

⇒ XO = YO + OZ

In triangle XYO,

⇒ XO = OY

So the triangle XYO is an isosceles triangle

⇒ So, \(\angle\)YXO = \(\angle\)XYO = \({30}^\circ\)

⇒ and \(\angle\)XYO = \(\angle\)XYZ

⇒ \(\angle\)XYZ = \({30}^\circ\)

Therefore, the required value is \({30}^\circ\)