Question 40

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

Solution

Given : ∠ACD = 114° and ∠ABC = (1/2)∠BAC

To find : ∠BAC = $$2\theta$$ = ?

=> $$\angle ABC = \theta$$

Solution : Using exterior angle property

=> ∠A + ∠B = ∠ACD

=> $$2\theta+\theta=114^\circ$$

=> $$\theta=\frac{114}{3}=38^\circ$$

$$\therefore$$ ∠BAC = $$2\theta=2\times38=76^\circ$$

=> Ans - (C)

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