In an isosceles triangle ABC, AB = AC, XY || BC.

If ∠A = 30°, then ∠BXY = ?

The correct option is 75°.

Step-by-step Explanation:

Step 1: Determine the base angles of the isosceles triangle

We are given an isosceles triangle ABC where:

$AB=AC$

In any triangle, angles opposite to equal sides are equal. Therefore, the base angles opposite to sides AB and AC are equal:

$\angle B=\angle C$

Step 2: Apply the angle sum property of a triangle

The sum of all interior angles in any triangle is 180°:

$\angle A+\angle B+\angle C=180°$

Given that ∠A = 30° and ∠C = ∠B, we substitute these values into the equation:

$30°+\angle B+\angle B=180°$

Simplify the equation:

$30°+2\angle B=180°$

Subtract 30° from both sides of the equation:

Divide by 2 to find the measure of ∠B:

$\angle B=75°$

Step 3: Analyze the parallel lines and transversal

We are given that XY || BC, where X lies on AB and Y lies on AC. Since XY is parallel to BC, the transversal line AB creates corresponding angles that are equal:

$\angle AXY=\angle B$

Since ∠B = 75°, the corresponding angle is:

$\angle AXY=75°$

Therefore, the angle corresponding to the base angle at the parallel intersection, ∠BXY (or ∠AXY), is 75°.