The second angle in a triangle is one third as large as the first. The third angle is two thirds as large as the first angle. Find the angle...

Let the angles of the triangle measure a, b and c. 

Since, the second angle is one third as large as the first angle, we get: 

b = 1/3 a

Similarly, the third angle is two third as large as the first angle, thus:

c = 2/3 a

Since, the sum of all the angles of a triangle is 180 degrees, we get,

a + b + c = 180 degrees

substituting the values of a,b and c into the equation, we get:

a + 1/3 a + 2/3 a = 180

or, 2 a = 180

or a = 180/2 = 90 degrees

and hence, b = 1/3 a = 1/3 x 90 = 30 degrees

and c = 2/3 a = 2/3 x 90 = 60 degrees

Thus, this is a right angled triangle, with angles measuring 30, 60 and 90 degrees.

Hope this helps.