Question

in isosceles triangle the base angle are equal to the vertex angle is 3 times the base angle.find each angle of triangle.

Answer 1

since it's a isosceles triangle then both the base angles will be equal.
let base angle=A,

then
vertex angle=3A,

By angle sum property ,

A+A+3A=180°,

5A=180°,

A=36°,

therefore

base angles =36° and 36°,

vertex angle=3×36°=108°

Answer 2

Let the base angle be x
So the vertex angle and the other base angle is x and 3x respectively
We know that the sum of interior angle of a triangle is 180
So,
$x + x + 3x = 180 \\ 5x = 180 \\ x = \frac{180}{5} \\ x = 36$
So the two equal angles are 36° and the larger angle is 3 × 36 = 108°