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In ΔABC, D is a point on side BC such that ∠ADC = 2∠BAD. If ∠A = 80° and ∠C = 38°, then what is the measure of ∠ADB? 

In ΔABC, D is a point on side BC such that ∠ADC = 2∠BAD. If ∠A = 80° and ∠C = 38°, then what is the measure of ∠ADB?  Correct Answer 56° 

Given:

In ΔABC, D is a point on side BC

∠ADC = 2∠BAD

∠A = 80°  and ∠C = 38° 

Concept used:

The sum of all angles in any triangle is to be 180°

The sum of two opposite angles = external angles

Explanation:

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According to the question,

80° + 38° + ∠B = 180° 

⇒ ∠B = 62° 

∵ ∠ADC = 2∠BAD

if ∠BAD = x than ∠ADC = 2x

By theorm,

∠BAD + ∠ABD = ∠ADC

⇒ x + 62° = 2x

⇒ x = 62° 

In ΔABD,

∠ABD + ∠BAD + ∠ADB = 180° 

⇒ 62° + 62° + ∠ADB = 180° 

⇒ ∠ADB = 56° 

∴ The measure of ∠ADB is 56° .

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