Question : In $\triangle \mathrm{STU}, \mathrm{SX}$ is the median on $\mathrm{TU}$. If $\mathrm{SX}=\mathrm{TX}$, then what is the value of $\angle \mathrm{TSU}$?
Option 1: 75°
Option 2: 45°
Option 3: 60°
Option 4: 90°
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Correct Answer: 90°
Solution :
In $\triangle$STU, SX is the median.
So, TX = XU (median property)
SX = TX (given)
So, $\triangle$STX is an isosceles triangle.
Let $\angle$STX = $\angle$TSX = $\theta$
⇒ $\angle$SXU = $2\theta$ (exterior angle)
Similarly in $\triangle$SXU,
SX = XU
$\triangle$SXU is an isosceles triangle.
Let $\angle$SUX = $\angle$USX = $\alpha$
⇒ $\angle$SXT = $2\alpha$ (exterior angle)
Now,
$2\theta + 2\alpha = 180° $ (Linear pair)
$⇒\theta + \alpha = 90°$
So, $\angle$TSU $= \theta +\alpha = 90°$
Hence, the correct answer is 90°.
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