In ABC a line is drawn from A to intersect the opposite side BC at D What is m ang BAD such that AC ...........

Quantitative Aptitude ( CCS) Geometry

In ?ABC, a line is drawn from A to intersect the opposite side BC at D. What is m∠BAD such that AC = CD and m∠CAB = m∠ABC + 60°?

15°

30°

20°

25°

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Explanation:

? AC = CD, m∠ADC = m∠ACD
m∠BAD = m∠CAB − m∠CAD
= m∠CAB – m∠ADC
Using exterior angle theorem, m∠ADC = m∠BAD + m∠ABD
∴ m∠BAD = m∠CAB – (m∠BAD + m∠ABD)
m∠ABD = m∠ABC
∴ 2(m∠BAD) = m∠CAB − m∠ABC = 60°
∴ m∠BAD = 30°