Question

in an isosceles triangle,the base angles are equal and the vertex angle is twice the base angle.find the measure of each angle.what typevofvtriangle is it?

Answer 1

since the sum of the interior angles of any triangle adds up to
180
∘
and also the base angles of an isosceles triangle are equal,we may let the base angles be
x
, then the vertex angle is
2
x
.
∴
x
+
x
+
2
x
=
180
∘
.
∴
x
=
45
∘
.
Therefore the vertex angle is
90
∘
.

Answer 2

Since the base angles of isosceles triangle are equal, therefore,
Let the base angles be 'x' and 'x'.
Also it is given that the vertex angle is twice its base angle, therefore,
Let the vertex angle be '2x'.

Using Angle Sum Property of Triangle,
x + x + 2x = 180°
4x = 180°
x = 180°/4
x = 45°

Now, base angles = x = 45°
& vertex angle = 2x = 90°.

Hence, it is a Right Angled Triangle.