Mathematics

In. triangle ABC,$$\angle A$$ + $$\angle B$$ = 144 and$$\angle A$$ + $$\angle C$$ = 124.
Calculate smallest angle of the triangle.


ANSWER

$$36^o$$


SOLUTION
$$\angle A + \angle B = 144$$...(I)
$$\angle A + \angle C = 124$$...(II)
In triangle ABC,
$$\angle A  + \angle B + \angle C = 180 $$
Add, I and II,
$$\angle A + \angle B + \angle A + \angle C = 144+ 124$$
$$180 + \angle A = 268 $$
$$\angle A = 268 - 180 $$
$$\angle A = 88$$
Put this value in (I)
$$\angle A + \angle B = 144$$
$$88 + \angle B = 144$$
$$\angle B = 56$$
Put this value in (II)
$$\angle A + \angle C = 124$$
$$88 + \angle C = 124$$
$$\angle C = 36$$
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