Question 119

ABC is a triangle with AC = BC and ∠ABC = 50°. The side BC is produced to D so that BC = CD. ∠BAD is

Solution

Given : BC = AC = CD and $$\angle$$ABC = 50°

To find : $$\angle$$BAD = ?

Solution : Since, BC = AC, => $$\angle$$ABC = $$\angle$$CAB = 50°

=> $$\angle$$ACB = 180° - 100° = 80°

Also, $$\triangle$$ACD is isosceles

=> $$\angle$$CAD = $$\angle$$ADC

=> $$\angle$$ACB = 2$$\angle$$CAD

=> $$\angle$$CAD = 80°/2 = 40°

$$\therefore$$ $$\angle$$BAD = 50° + 40° = 90°

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