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°
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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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