Question

In an isosceles triangle, if the vertex angle is four times the sum of the base angles, then what are the angles of the triangle?
What will be this triangle classifed as according to angles?

Answer 1

Since this is an isosceles triangle, the base angles will be equal.Let the base angle be $x$ and $x$.
Then, vertex angle
$=4\times$ sum of base angles
$=4\times (x+x)$
$=4\times 2x=8x$
Now, from angle sum property of triangle
$8x+x+x={180}^{\circ }$
$⟹10x={180}^{\circ }$
$⟹x={18}^{\circ }$

Hence the angles of the triangle are ${18}^{\circ },{18}^{\circ }$ and $[4\times (18+18\left)\right]={144}^{\circ }$

Since one of the angles is greater than ${90}^{\circ }$, this is an obtuse triangle.