If the measures of angles of a triangle are in the ratio of 3 : 4 : 5, what is the measure of the smallest angle of the triangle?

Question

Philoid · Accepted Answer

Let,

∠1, ∠2 and ∠3 be the angles of the triangle which are in the ratio 3: 4: 5 respectively.

∠1 = 3k

∠2 = 4k

∠3 = 5k

We know that,

∠1 + ∠2 + ∠3 = 180^o

3k + 4k + 5k = 180^o

k = 15^o

So,

∠1 = 3 * 15^o = 45^o

∠2 = 4 * 15^o = 60^o

∠3 = 5 * 15^o = 75^o

Thus, smallest angle is 45^o.