In Δ ABC ∠B= ∠C and ray AX bisects the exterior angle ∠DAC. If ∠DAX =70°, then ∠ACB =
A. 35°
B. 90°
C. 70°
D. 55°
Answers
Given: In Δ ABC ∠B = ∠C and ray AX bisects the exterior angle ∠DAC and ∠DAX = 70°.
To Find : ∠ACB
Proof :
Ray AX bisects exterior angle ∠DAC.
∴ ∠CAD = 2 × ∠DAX
∠CAD = 2 × 70°
∠CAD = 140°
By exterior angle theorem, If a side of a triangle is produced, the exterior angle so formed is equal to the sum of the two interior opposite angles :
Ext. ∠CAD = ∠B + ∠C
140° = ∠C + ∠C
[Given : ∠B = ∠C]
140° = 2∠C
∠C = 140°/2
∠C = 70°
∠ACB = 70°
Hence, ∠ACB is 70°.
Among the given options option (C) 70° is correct.
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Answer:
Step-by-step explanation:
Proof :
Ray AX bisects exterior angle ∠DAC.
∴ ∠CAD = 2 × ∠DAX
∠CAD = 2 × 70°
∠CAD = 140°
By exterior angle theorem, If a side of a triangle is produced, the exterior angle so formed is equal to the sum of the two interior opposite angles :
Ext. ∠CAD = ∠B + ∠C
140° = ∠C + ∠C
[Given : ∠B = ∠C]
140° = 2∠C
∠C = 140°/2
∠C = 70°
∠ACB = 70°