In ΔABC, D is a point on BC such that ∠ADB = 2∠DAC, ∠BAC = 70° and ∠B = 56°. What is the measure of ∠ADC?
A. 54°
B. 81°
C. 74°
D. 72°
Answer: Option D
Solution (By Examveda Team)
Let ∠DAC = x
∠ADB = 2x
∠ACD + ∠DAC = ∠ADB
∠ACD + x = 2x
∠ACD = 2x - x = x
In ΔABC
∠A + ∠B + ∠C = 180°
70° + 56° + ∠C = 180°
∠C = 54°
∠ADC = 180° - 2x
= 180° - 2 × 54°
= 180° - 108°
= 72°
This Question Belongs to Arithmetic Ability >> Geometry
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