In Δ ABC, D is a point on BC such that ∠ ADB = 2 ∠ DAC, ∠ BAC = 70º and ∠ B = 56º. What is the measure of ∠ ADC?

In Δ ABC, D is a point on BC such that ∠ ADB = 2 ∠ DAC, ∠…

In $\Delta$ ABC, D is a point on BC such that $\angle$ ADB = 2 $\angle$ DAC, $\angle$ BAC = 70º and $\angle$ B = 56º. What is the measure of $\angle$ ADC?

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 72º

In $\Delta$ ABC,

$\angle$ A + $\angle$ B + $\angle$ C = 180

70 + 56 + $\angle$ C = 180

$\angle$ C = 180 - 126 = 54°

$\angle$ ADB = $\angle$ DAC + $\angle$ ACD (Exterior angle sum property)

$2\theta$ = $\theta$ + 54

$\theta$ = 54°

$\angle$ ADC = 180 - $2\theta$ (Linear pair with $\angle$ ADB)

$\angle$ ADC = 180 - 108 = 72°

SSC CGL 2022 PYQ — Question 21