ABC is an isosceles triangle with AB = AC. The side BA is produced to D such that AB = AD. If ∠ABC = 30°, then ∠BCD is equal to
A. 45°
B. 90°
C. 30°
D. 60°
Answer: Option B
Solution(By Examveda Team)
According to question,In ΔABC
Exterior angle CAD = ∠ABC + ∠ACB
CAD = 2∠ABC (∵ ∠ABC = ∠ACB)
CAD = 2 × 30°
CAD = 60°
In ΔCAD,
∠ACD = ∠ADC = $$\frac{{180 - \angle {\text{CAD}}}}{2}$$ = 60°
⇒ ∠BCD = ∠ACD + ∠BCA
⇒ ∠BCD = 60° + 30°
⇒ ∠BCD = 90°
Related Questions on Triangles
If ABC and PQR are similar triangles in which ∠A = 47° and ∠Q = 83°, then ∠C is:
A. 50°
B. 70°
C. 60°
D. 80°
In the following figure which of the following statements is true?
A. AB = BD
B. AC = CD
C. BC + CD
D. AD < Cd
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