AP EAMCET · Maths · Properties of Triangles
In a \(\triangle A B C, \angle C=60^{\circ}\) and \(\angle A=75^{\circ}\). If \(D\) is a point on \(A C\) such that the area of \(\triangle B A D\) is \(\sqrt{3}\) times the area of \(\triangle B C D\), then the measure of \(\angle A B D\) is
- A \(30^{\circ}\)
- B \(45^{\circ}\)
- C \(60^{\circ}\)
- D \(90^{\circ}\)
Answer & Solution
Correct Answer
(A) \(30^{\circ}\)
Step-by-step Solution
Detailed explanation
In a \(\triangle A B C\), it is given the angles \(A=75^{\circ}\) and \(C=60^{\circ}\) and \(\quad \triangle B A D=\sqrt{3}(\triangle B C D) \Rightarrow(A D)=\sqrt{3}(C D)\) \(\Rightarrow \quad \frac{A D}{C D}=\sqrt{3}\) As angle \(B=45^{\circ}\), Now let…
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