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 isÂ
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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