Question : In the given figure, if KI = IT and EK = ET, then $\angle$ TEI =________.
Option 1: 75°
Option 2: 125°
Option 3: 105°
Option 4: 150°
Correct Answer: 105°
Solution :
KI = IT and EK = ET
$\angle$ KET = 150°
In $\triangle$ KEI and $\triangle$ TEI,
KI = IT [Given]
EK = ET [Given]
EI = EI [Common]
So, $\triangle$ KEI $\cong$ $\triangle$ TEI,
⇒ $\angle$ KEI = $\angle$ TEI
Now,
$\angle$ KET + $\angle$ KEI + $\angle$ TEI = 360°
⇒ 150° + 2 × $\angle$ TEI = 360°
⇒ 2 $\angle$ TEI = 210°
⇒ $\angle$ TEI = 105°
Hence, the correct answer is 105°.
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