The ratio between a base angle and the vertical angle of an isosceles triangle is 1:4. Find each angle of the triangle.

Given : 

The ratio of base angle to vertical angle $= 1:4$

To find : 

We have to find each angle of the triangle.

Solution :

In an Isosceles triangle base angles are equal.

So, let two base angles be x, x and vertical angle be 4x.

Sum of all angles of triangle $= 180°$

$x + x + 4 x  =  180°$

$2 x + 4 x = 180°$

$6 x = 180°$

$x = \frac{180}{6}$

$x = 30°$

$4 x = 4\times30  = 120°$

So, base angle $ = 30°$    ;    Vertical angle $= 120°$

Therefore, the angles of the triangle are 30°, 30° and 120°.