Question

In an isosceles triangle, the vertex angle is 4 times either of the base angle. Find the angles of the triangle

Answer 1

HEY DEAR ... ✌️

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⏺️Answer :- There are infinite triangles . ∆

⏺️ Explanation :-

Let 2 equal angles be x & x

So third angle will be 4x..

x + x + 4x = 180°

=> 6x = 180°

=> x= 30°

So, its angles will be 30°, 30° & 120°

But its sides can be of any measure, but 2 of its sides will be equal in length…

And all these triangles will be similar.

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HOPE , IT HELPS ... ✌️

Answer 2

let angles on base of triangle be x & y
But x= y. ...( isosceles triangle theorem )...(1)
therefore, vertex angle = 4x...[fromgiven and (1)]...(2)
Now,
by angle sum property of triangle
4x+x+x=180°
6x=180°
x=180°/6
x=30°
now from given angles on base are 30° and 30°
vertex angle = 4×30°=120°
ANS: angles of triangle are 30°, 30° and 120°.