The sum of two angles of a triangle is 116° and their difference is 24°. The measure of smallest angle of the triangle is

Let the angles of the triangle be $$\alpha,\beta$$ and $$\theta$$

Here, $$\alpha+\beta=116^\circ$$ --------(i)

and $$\alpha-\beta=24^\circ$$ -----------(ii)

Adding equations (i) and (ii)

=> $$2\alpha=116+24=140^\circ$$

=> $$\alpha=\frac{140}{2}=70^\circ$$

Substituting it in equation (i), => $$\beta=116-70=46^\circ$$

Also, in a triangle, $$\alpha+\beta+\theta=180^\circ$$

=> $$70^\circ+46^\circ+\theta=180^\circ$$

=> $$\theta=180-116=64^\circ$$

Thus, the smallest angle = $$\beta = 46^\circ$$

=> Ans - (C)