The measures of two angles of a triangle are in the ratio 3 : 7. If the sum of these two measures is equal to the measure of the third angle, then find the smallest angle.

Given: 

Ratio of two angle of triangle = 3 : 7 

Third angle = Sum of measure of other two angles 

Concept Used: 

Sum of all the interior angle of a triangle is $$180^\circ$$ 

Solution: 

Let the two angle be 3x and 7x.

then the third angle = 3x + 7x = 10x 

Now,

3x + 7x + 10x = 180 

20x = 180 

x = $$\frac{180}{20}$$​ = 9 

Thus, the smallest angle = $$3\times x = 3 \times 9 =\bf 27^\circ$$​​