Question 163

ABC is a triangle and the sides AB, BC and CA are produced to E, F and G respectively. If $$\angle$$CBE = $$\angle$$ACF = 130° then the value of $$\angle$$GAB is

Solution

Using linear pair property :

=> $$\angle$$ACB + $$\angle$$ACF = 180°

=> $$\angle$$ACB = 180°-130° = 50°

Similarly, $$\angle$$ABC = 50°

Now, in $$\triangle$$ABC

$$\angle$$BAC = 180°-(50°+50°) = 180°-100°

=> $$\angle$$BAC = 80°

Again using linear pair property, we get :

$$\angle$$GAB + $$\angle$$BAC = 180°

=> $$\angle$$GAB = 180°-80° = 100°

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