In a triangle ABC the side BC is extended up to D Such that CD AC if ang BAD 109 deg and ang ACB 72 ...........

Quantitative Aptitude ( CCS) Geometry

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

35°

60°

40°

45°

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Explanation:

We know that, Exterior angle is sum of opposite interior angles
∴ ∠CAD + ∠ADC = ∠ACB = 72°
2∠ADC = 72°
[? AC = DC ⇒ ∠CAD = ∠ADC]
∠ADC = 36°
In ΔABD, we know that
∠ABC = 180° – ∠BAD – ∠ADB
= 180° – 109° – 36° = 35°