Question : In an isosceles $\triangle ABC$, $AB = AC$, $XY || BC$. If $\angle A=30°$, then $\angle BXY$?
Option 1: 75°
Option 2: 30°
Option 3: 150°
Option 4: 105°
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Correct Answer: 105°
Solution : Given: In an isosceles $\triangle ABC$, $AB = AC$. $\angle BAC=30°$ We know that the sum of all the angles in a triangle is 180°. In an isosceles $\triangle ABC$, $AB = AC$. So, $\angle ABC=\angle ACB$ $\angle ABC + \angle ACB + \angle BAC = 180°$ $⇒2\angle ABC + 30° = 180°$ $⇒\angle ABC=\frac{180°–30°}{2}$ $⇒\angle ABC=\frac{150°}{2}=75°$ Since $XY || BC$, $\angle AXY=\angle ABC=75°$ $\angle BXY=180°–\angle ABC$ $⇒\angle BXY=180°–75°$ $⇒\angle BXY=105°$ Hence, the correct answer is 105°.
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