Question 78

In ΔABC, AC = BC and ∠ABC = $$50^\circ$$, the side BC is produced to D so that BC = CD then the value of ∠BAD is

Solution

AC = BC

$$\angle ABC = \angle BAC = 50\degree$$

$$\angle ACB = 180\degree - 100\degree = 80\degree$$

$$\angle ACD = 180\degree - 80\degree = 100\degree$$

$$\angle CAD = \angle CDA = \frac{80\degree}{2} = 40\degree$$

$$\angle BAD = \angle BAC + \angle CAD = 50\degree + 40\degree = 90\degree$$

So, the answer would be option c)$$90^\circ$$

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