Question 106

The side $$BC$$ of a triangle ABC is extended to D. If $$\angle$$ ACD = $$112^\circ$$ and $$\angle$$ B= $$\frac{3}{4}$$ of $$\angle$$ A, then the measure of $$\angle$$ B is 

Solution

Given $$\angle B = \frac{3}{4}$$ of $$\angle A$$ ......(1)

An exterior angle of a triangle is equal to sum of the opposite interior angles.

$$\therefore \angle A + \angle B = 112^{\circ}$$

Substitute equation (1) in the above equation

$$\frac{4}{3} (\angle B) + \angle B = 112^{\circ}$$

$$(\angle B)(\frac{7}{3}) = 112^{\circ}$$

$$\angle B = 48^{\circ}$$

Hence, option C is the correct answer.


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