The side BC of ΔABC is produced to D. If ΔACD =114° and \angleABC = (1 / 2) \angleBAC, then what is the value (in degrees) of ∠BAC ?

SSC CGL Model Paper 16

Question : 65 of 100

Marks: +1, -0

The side BC of ΔABC is produced to D. If ΔACD =114° and

∠ABC = (1 / 2) ∠BAC

, then what is the value (in degrees) of ∠BAC ?

Solution:

∠ACD = 114°

∠\ABC=∠\BCA/2

Let ∠BAC = x

∠\ABC=x/2

∠ABC + ∠BAC =114°
⇒

x+x/2=114°

⇒

{3x}/2=114°

⇒

x = 3 8 °× 2

x = 7 6 °

So, ∠BAC = 76°

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