In a triangle ABC, the side BC is extended up to D such that CD = AC. If ∠BAD = 109° and ∠ACB = 72° then the value of ∠ABC is
A. 35°
B. 60°
C. 40°
D. 45°
Answer: Option A
Solution(By Examveda Team)
According to question,Given :
∠BAD = 109°
∠ACB = 72°
∴ ∠ACD = 180° - 72°
∠ACD = 108°
∴ AC = CD
∠CAD = ∠CDA
In ΔCDA
∠CAD + ∠CDA + ∠DCA = 180°
2∠CAD + 108° = 180°
2∠CAD = 180° -108°
2∠CAD = 72°
∠CAD = $$\frac{{{{72}^ \circ }}}{2}$$
∠CAD = 36°
∴ ∠CAB = 109° - 36°
∠CAB = 73°
In ΔABC
∠ABC + ∠ACB + ∠CAB = 180°
∠ABC + 72° + 73° = 180°
∠ABC + 145° = 180°
∠ABC = 180° - 145°
∠ABC = 35°
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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