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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°.
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