In △XYZ, XO is the median and XO = \(\frac{1}{2}\) YZ. If ∠YXO = 30°, then what is the value of ∠XYZ?

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 07 Dec 2022 Shift 3)

Answer 1

Given:

In △XYZ, XO is the median and XO = \(\frac{1}{2}\) YZ.

∠YXO = 30°

Calculations:
F2 Vinanti SSC 01.06.23 D1
According to question,

In ∆ XOY,

As XO is median, So

⇒ YO = OZ

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

⇒ XO = YO = OZ

In ∆ XYO,

⇒ XO = OY

So the triangle XYO is an isosceles triangle

⇒ So, ∠YXO = ∠XYO = 30°

⇒ and ∠XYO = ∠XYZ

⇒ Therefore, ∠XYZ = 30°

⇒ Hence, The Required value is 30°