Question : In an isosceles $△ A B C$ , $A B = A C$ , $X Y | | B C$ . If $∠ A = 30 °$ , then $∠ B X Y$ ?
Option 1: 75°
Option 2: 30°
Option 3: 150°
Option 4: 105°

Question

Question : ABC is an isosceles triangle such that AB = AC, $∠$ ABC = 55°, and AD is the median to the base BC. Find the measure of $∠$ BAD.

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Answer 1

Correct Answer: 105°

Solution : Given: In an isosceles $△ A B C$ , $A B = A C$ .
$∠ B A C = 30 °$
We know that the sum of all the angles in a triangle is 180°.

In an isosceles $△ A B C$ , $A B = A C$ .
So, $∠ A B C = ∠ A C B$
$∠ A B C + ∠ A C B + ∠ B A C = 180 °$
$\Rightarrow 2 ∠ A B C + 30 ° = 180 °$
$\Rightarrow ∠ A B C = \frac{180 ° - 30 °}{2}$
$\Rightarrow ∠ A B C = \frac{150 °}{2} = 75 °$
Since $X Y | | B C$ , $∠ A X Y = ∠ A B C = 75 °$
$∠ B X Y = 180 ° - ∠ A B C$
$\Rightarrow ∠ B X Y = 180 ° - 75 °$
$\Rightarrow ∠ B X Y = 105 °$
Hence, the correct answer is 105°.

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Question : In an isosceles △ABC, AB=AC, XY||BC. If ∠A=30°, then ∠BXY?Option 1: 75°Option 2: 30°Option 3: 150°Option 4: 105°

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Question : In an isosceles $△ A B C$ , $A B = A C$ , $X Y | | B C$ . If $∠ A = 30 °$ , then $∠ B X Y$ ?
Option 1: 75°
Option 2: 30°
Option 3: 150°
Option 4: 105°