Given
One angle of an isoceles triangle is 70.
Two angles are same.
Therefore the possibilities for the other two angles are 70, 40 (or) 55, 55.

'a' is true.
An isosceles triangle need not have three equal sides.

No, It is not possible with angles 90°, 90°, 0°.
Because there cannot be two right angles in a triangle

All angles are right angles two triangles formed.
Both are Isoceles right angled triangle.

Given
One angle of an isoceles triangle = 124°
The sum of three angles of a triangle is = 180°
= 180° - 124° = 56°
Sum of other two angles are = 56°
Two angles are same = 56°/ 2 = 28°
Other angles are 28°, 28°.

Isoceles right angled Triangle
Two angles are equal and one angle is right angle.
Therefore the three angles are 45^o, 45^o, 90^o.

All angles are equal.
I am an equilateral triangle.

i)

3 angles are acute and 2 sides are equal.
Type: Isoceles acute angled triangle.
ii)

Three sides are different and one angle is right angle.
Type: Scalene right angled triangle.
iii)

Two sides are equal and one angle is obtuse.
Type: Isoceles obtuse angled triangle.
iv)

Two sides are equal and one angle is right angle.
Type: Isoceles acute angled triangle.
v)

Three sides are equal and Three angles are acute.
Type: Equilateral right angled triangle.
vi)

All sides are different and one angle is obtuse.
Type: Scalene obtuse angled triangle.

i)
 
All sides are equal.
Type: Equilateral triangle.
ii) 

Three sidesare different lengths,
Type: Scalene triangle .
iii)

Two sides are equal,
Type : Isoceles triangle.
iv)
 
Three sides are different lengths.
Type: Scalene triangle.

(a) Three Sides : \(\overline{\mathrm{AB}}, \overline{\mathrm{BC}}, \overline{\mathrm{CA}}\)
(b) Three Angles : \( \angle \mathbf{A B C}, \angle \mathbf{B C A}, \angle \mathbf{C A B} \) or \( \angle \mathbf{A}, \angle \mathbf{B}, \angle \mathbf{C} \)
(c) Three Vertices : A, B, C