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°
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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