The measures of two angles of a triangle are in the ratio 4 : 5. If the sum of these two measures is equal to the measure of the third angle, find the smallest angle.

Solution:

Two angles of triangle
= 4x and 5x (let)
According to the question.
2(4x+ 5x) = 180^∘
⇒ 18x= 180^∘
⇒ x = 180^∘/18 = 10^∘
:. The smallest angle
= 4x = 4*10 = 40^∘
Then the answer is 40^∘.