Question 63

In a $$\triangle$$ABC, $$\angle$$ABC = 2$$\angle$$CAB, If the side BC is extended to D and $$\angle$$ACD = 126$$^\circ$$, then $$\angle$$CAB is:

Solution

Let $$\angle$$CAB = x

Given,  $$\angle$$ABC = 2$$\angle$$CAB

$$=$$>  $$\angle$$ABC = 2x

In $$\triangle$$ABC,

$$\angle$$ACD is the exterior angle at point C which is equal to the sum of the interior angles at points A and B

$$=$$>  $$\angle$$ABC + $$\angle$$CAB = $$\angle$$ACD

$$=$$>  2x + x = 126$$^\circ$$

$$=$$>  3x = 126$$^\circ$$

$$=$$>   x = 42$$^\circ$$

$$=$$>  $$\angle$$CAB = 42$$^\circ$$

Hence, the correct answer is Option B


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